Alexandrov topology
cofinite topology
semiregular
sheaf
disjoint set
ball
trivial topology
neighborhood
subspace topology
domain
π-system
Kolmogorov
Kolmogorov space
topology
disjoint
T₁
compact
continuous function
discrete
hyperconnected
metacompact
valuation
pseudointersection
equivalence class
discrete topology
Grothendieck topology
discrete set
disjoint union
group
Hintikka set
filter
mathematical group
normal space
open-chain
quotient set
connection
germ
symmetric difference
acyclic
hyperconnection
Lindelöf covering theorem
generic property
paracompact
base
Helly family
ring
Baire space
setoid
pole
pointless topology
convex set
topologically
extreme point
boundary
interior
wedge sum
underlying set
lake of Wada
equivalence
prevariety
isotopological
unicoherent
standard topology
holomorphic
monad
interlayering
Cantor-Bendixson theorem
Helly's theorem
Lindelöf space
hull
multialgebra
open
spread
unfold
Venn diagram
Grothendieck universe
spread out
associahedron
topological space
carrier set
metaset
diffeology
Hausdorff space
second-countable
initial topology
cut-set
algebra
overlap
Seifert surface
regular space
topologized
left total
axiom of union
hyperbolic geometry
Euler diagram
knot
semiregular
Kolmogorov
disjoint
T₁
compact
discrete
hyperconnected
metacompact
open-chain
acyclic
paracompact
isotopological
unicoherent
holomorphic
second-countable
topologized
left total
topologically
Alexandrov topology
cofinite topology
sheaf
disjoint set
ball
trivial topology
neighborhood
subspace topology
domain
π-system
Kolmogorov space
topology
continuous function
valuation
pseudointersection
equivalence class
discrete topology
Grothendieck topology
discrete set
disjoint union
group
Hintikka set
filter
mathematical group
normal space
quotient set
connection
germ
symmetric difference
hyperconnection
generic property
base
Helly family
ring
Baire space
setoid
pole
pointless topology
convex set
extreme point
boundary
interior
wedge sum
underlying set
lake of Wada
equivalence
prevariety
standard topology
monad
interlayering
Lindelöf space
hull
multialgebra
Venn diagram
Grothendieck universe
associahedron
topological space
carrier set
metaset
diffeology
Hausdorff space
initial topology
cut-set
algebra
Seifert surface
regular space
axiom of union
hyperbolic geometry
Euler diagram
knot
open
spread
unfold
spread out
overlap
noun
- An abstract construct in topology that associates data to the open sets of a topological space, together with well-defined restrictions from larger to smaller open sets, subject to the condition that compatible data on overlapping open sets corresponds, via the restrictions, to a unique datum on the union of the open sets.
- A quantity of arrows, usually twenty-four.
- A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.
- A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.
- Any collection of things bound together.
- A sheave.
verb
noun
- The set of points in a topological space lying within some open set containing a given point.
- Any sport or game involving a ball; its play, literally or figuratively.
- A solid or hollow sphere, or roughly spherical mass.
- A competitive event among young African-American and Latin American LGBTQ+ people in which prizes are awarded for drag and similar performances. See ball culture.
- Nonsense.
- A very enjoyable time.
- An opportunity to launch the pinball into play.
- The globe; the earthly sphere.
- A pass; a kick of the football towards a teammate.
- A pitch that falls outside of the strike zone.
- The front of the bottom of the foot, just behind the toes.
- Courage.
- A large pill, a form in which medicine was given to horses; a bolus.
- A formal dance.
- The set of points in a metric space of any number of dimensions lying within a given distance (the radius) of a given point.
- A single delivery by the bowler, six of which make up an over.
- In 3-dimensional Euclidean space, the volume bounded by a sphere.
- A leather-covered cushion, fastened to a handle called a ballstock; formerly used by printers for inking the form, then superseded by the roller.
- A roundish, protuberant portion of some part of the body.
- An object that is the focus of many sports and games, in which it may be thrown, caught, kicked, bounced, rolled, chased, retrieved, hit with an instrument, spun, etc., usually roughly spherical but whose size, weight, bounciness, colour, etc. differ according to the game
- A jacketed non-expanding bullet, typically of military origin.
- One thousand US dollars.
- A quantity of string, thread, etc., wound into a spherical shape.
intj
verb
- To reject from a fraternity or sorority. (Short for blackball.)
- To form or wind into a ball.
- To gather balls which cling to the feet, as of damp snow or clay; to gather into balls.
- To punish by affixing a ball and chain.
- To have sexual intercourse with.
- To heat in a furnace and form into balls for rolling.
- To play basketball.
- To be hip or cool.
noun
- Alternatively: An open set which contains some specified point.
- The infinitesimal open set of all points that may be reached directly from a given point.
- A set containing an open set which contains some specified point.
- The set of all the vertices adjacent to a given vertex.
- The residential area near one's home.
- The inhabitants of a residential area.
- A formal or informal division of a municipality or region.
- A set containing an open ball which contains a specified point.
- An approximate amount.
- The quality of physical proximity.
- Alternatively: An open ball which contains some specified point.
noun
- An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.
- The set of all possible mathematical entities (points) where a given function is defined.
- A ring with no zero divisors; that is, in which no product of nonzero elements is zero.
- The highest rank in the classification of organisms, above kingdom; in the three-domain system, one of the taxa Bacteria, Archaea, or Eukaryota.
- A geographic area owned or controlled by a single person or organization.
- A collection of DNS or DNS-like domain names consisting of a delegated domain name and all its subdomains.
- The set of input (argument) values for which a function is defined.
- The collection of computers identified by a domain's domain names.
- A collection of information having to do with a domain, the computers named in the domain, and the network on which the computers named in the domain reside.
- A folded section of a protein molecule that has a discrete function; the equivalent section of a chromosome
- A small region of a magnetic material with a consistent magnetization direction.
- A group of related items, topics, or subjects.
- Such a region used as a data storage element in a bubble memory.
- A form of technical metadata that represent the type of a data item, its characteristics, name, and usage.
- A field or sphere of activity, influence or expertise.
- Any DNS domain name, particularly one which has been delegated and has become representative of the delegated domain name and its subdomains.
noun
- Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.
- The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
- The topographical study of geographic locations or given places in relation to their history.
- The arrangement of nodes in a communications network.
- The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).
- The anatomical structure of part of the body.
adj
- Such that every open cover of the given set has a finite subcover. In a Euclidean space this is equivalent to a Closed and bounded set.
- Having all necessary features fitting neatly into a small space.
- Brief; close; pithy; not diffuse; not verbose.
- Closely packed, i.e. packing much in a small space.
noun
- A small, slim folding case, often featuring a mirror, powder and a powderpuff; that fits into a woman's purse or handbag, or that slips into one's pocket.
- A broadsheet newspaper published in the size of a tabloid but keeping its non-sensational style.
- An agreement or contract.
verb
adj
- Having each singleton subset open: said of a topological space or a topology.
- Consisting of or permitting only distinct values drawn from a finite, countable set.
- Separate; distinct; individual; non-continuous.
- Having separate electronic components, such as individual diodes, transistors and resistors, as opposed to integrated circuitry.
- Having separate and independent channels of audio, as opposed to multiplexed stereo or quadraphonic, or other multi-channel sound.
- Disjunctive; containing a disjunctive or discretive clause.
- That can be perceived individually, not as connected to, or part of, something else.
noun
- A map from the class of open sets of a topological space to the set of positive real numbers including infinity.
- An assignment of truth values to propositional variables, with a corresponding assignment of truth values to all propositional formulas with those variables (obtained through the recursive application of truth-valued functions corresponding to the logical connectives making up those formulas).
- The process of estimating the value of a financial asset or liability.
- A measure of size or multiplicity.
- A structure, and the corresponding assignment of a truth value to each sentence in the language for that structure.
- An estimation of something's worth.
noun
- The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology.
- A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing).
- A union of sets which are already pairwise disjoint.
noun
- A non-empty upper set (of a partially ordered set) which is closed under binary infima (a.k.a. meets).
- self-restraint in speech.
- A device which separates a suspended, dissolved, or particulate matter from a fluid, solution, or other substance; any device that separates one substance from another.
- Any item, mechanism, device or procedure that acts to separate or isolate.
- A translucent object placed in the light path of a camera to remove certain wavelengths (colors), or a computer program that simulates such an effect.
- Electronics or software that separates unwanted signals (for example noise) from wanted signals or that attenuates selected frequencies.
verb
noun
- A set of sets that contains the empty set, all one-element sets for any element that is included in any of the sets, and the union of any group of sets that are elements where the intersections of those sets is non-empty.
- A feeling of understanding and ease of communication between two or more people.
- sexual intercourse
- A kinship relationship between people.
- An individual who is related to oneself, through either family or business.
- A drug dealer.
- The description for a Methodist denomination as a whole, as opposed to its constituent churches, circuits, districts and conferences.
- Coherence; lack of disjointedness
- The point at which two or more things are connected.
- A transfer from one transportation vehicle to another in scheduled transportation service
- An established communications or transportation link.
- The act of connecting.
noun
- An equivalence class that includes a specified function defined in an open neighborhood.
- The origin or earliest version of an idea or project.
- The small mass of cells from which a part of an organism develops, or a macroscopic but immature form of that part; a bud.
- The embryo of a seed, especially of a seed used as a cereal or grain. See Wikipedia article on cereal germ.
- A pathogen: a pathogenic microorganism, such as a bacterium or virus.
verb
noun
- A property that is true in some dense open subset of a given set.
- A property that is true almost everywhere in a given set (i.e., the set of points at which the property is not true is either of measure zero or a subset of a set of measure zero).
- Used other than figuratively or idiomatically: see generic, property.
noun
- The set of sets from which a topology is generated.
- A basic but essential component or ingredient.
- Foundation: a cosmetic cream to make the face appear uniform.
- A topological space, looked at in relation to one of its covering spaces, fibrations, or bundles.
- The smallest kind of cannon.
- A line in a survey which, being accurately determined in length and position, serves as the origin from which to compute the distances and positions of any points or objects connected with it by a system of triangles.
- The forces and relations of production that produce the necessities and amenities of life.
- The name of the controlling terminal of a bipolar transistor (BJT).
- Something from which other things extend; a foundation.
- A safe zone in the children's games of tag and hide-and-go-seek.
- The lowest side of a triangle or other polygon, or the lowest face of a cone, pyramid or other polyhedron laid flat.
- freebase cocaine
- A nucleotide's nucleobase in the context of a DNA or RNA biopolymer.
- The starting point of a logical deduction or thought; basis.
- In hand-to-hand balance, the person who supports the flyer; the person that remains in contact with the ground.
- A group of voters who almost always support a single party's candidates for elected office.
- A substance used as a mordant in dyeing.
- A material that holds paint or other materials together; a binder.
- A number raised to the power of an exponent.
- A supporting, lower or bottom component of a structure or object.
- Any of a class of generally water-soluble compounds, having bitter taste, that turn red litmus blue, and react with acids to form salts.
- The end of a leaf, petal or similar organ where it is attached to its support.
- A kind of skirt (often of velvet or brocade, but sometimes of mail or other armour) which hung from the middle to about the knees, or lower.
- A sequence of elements not jointly stabilized by any nontrivial group element.
- The lowermost part of a column, between the shaft and the pedestal or pavement.
- A morpheme (or morphemes) that serves as a basic foundation on which affixes can be attached.
- Synonym of radix.
- The game of prisoners' bars.
- The lowest third of a shield or escutcheon.
- The lower part of the field. See escutcheon.
- The place where decisions for an organization are made; headquarters.
- A permanent structure for housing military personnel and material.
- One of the four places that a runner can stand without being subject to being tagged out when the ball is in play.
adj
- Low in place or position.
- Morally reprehensible, immoral; cowardly.
- Not held by honourable service.
- Not considered precious or noble.
- Not classical or correct.
- Alloyed with inferior metal; debased.
verb
noun
- A family of sets that is closed under finite unions and differences.
- A circumscribing object, (roughly) circular and hollow, looking like an annual ring, earring, finger ring etc.
- An exclusive group of people, usually involving some unethical or illegal practices.
- An old English measure of corn equal to the coomb or half a quarter.
- A large circular prehistoric stone construction such as Stonehenge.
- A group of atoms linked by bonds to form a closed chain in a molecule.
- A piece of food in the shape of a ring.
- Any loud sound; the sound of numerous voices; a sound continued, repeated, or reverberated.
- A circular group of people or objects.
- A sound or appearance that is characteristic of something.
- A flexible band partly or wholly encircling the spore cases of ferns.
- A bird band, a round piece of metal put around a bird's leg used for identification and studies of migration.
- A planar geometrical figure included between two concentric circles.
- A chime, or set of bells harmonically tuned.
- The resonant sound of a bell, or a sound resembling it.
- A formation of various pieces of material orbiting around a planet or young star.
- The open space in front of a racecourse stand, used for betting purposes.
- The twenty-fifth Lenormand card.
- A pleasant or correct sound.
- An algebraic structure which consists of a set with two binary operations: an additive operation and a multiplicative operation, such that the set is an abelian group under the additive operation, a monoid under the multiplicative operation, and such that the multiplicative operation is distributive with respect to the additive operation.
- A diacritical mark in the shape of a hollow circle placed above or under the letter; a kroužek.
- In a jack plug, the connector between the tip and the sleeve.
- A round piece of (precious) metal worn around the finger or through the ear, nose, etc.
- A place where some sports or exhibitions take place; notably a circular or comparable arena, such as a boxing ring or a circus ring; hence the field of a political contest.
- Either of the pair of clamps used to hold a telescopic sight to a rifle.
- A hierarchical level of privilege in a computer system, usually at hardware level, used to protect data and functionality (also protection ring).
- An algebraic structure as above, but only required to be a semigroup under the multiplicative operation, that is, there need not be a multiplicative identity element.
- A telephone call.
- A burner on a kitchen stove.
- An instrument, formerly used for taking the sun's altitude, consisting of a brass ring suspended by a swivel, with a hole at one side through which a solar ray entering indicated the altitude on the graduated inner surface opposite.
verb
- To produce (a sound) by ringing.
- To produce the sound of a bell or a similar sound.
- To telephone (someone).
- To steal and change the identity of (cars) in order to resell them.
- To make (a bell, etc.) produce a resonant sound.
- To ride around (a group of animals, especially catle) to keep them milling in one place; hence (intransitive), to work as a drover, to muster cattle.
- to resound, reverberate, echo.
- Of a bell, etc., to produce a resonant sound.
- Of something spoken or written, to appear to be, to seem, to sound.
- To surround or fit with a ring, or as if with a ring.
- To produce music with bells.
- To enclose or surround.
- To attach a ring to, especially for identification.
- To make an incision around; to girdle; to cut away a circular tract of bark from a tree in order to kill it.
- To rise in the air spirally.
noun
- A fixed point relative to other points or lines.
- A telescope used to identify birds, aeroplanes or wildlife.
- Either of the two points on the earth's surface around which it rotates; also, similar points on any other rotating object.
- A construction by which an animal is harnessed to a carriage.
- A gun.
- Either of the states that characterize a bipolar disorder.
- A point of magnetic focus, especially each of the two opposing such points of a magnet (designated north and south).
- Originally, a stick; now specifically, a long and slender piece of metal or (especially) wood, used for various construction or support purposes.
- A type of basic fishing rod.
- A long sports implement used for pole-vaulting; now made of glassfiber or carbon fiber, formerly also metal, bamboo and wood have been used.
- Pole position.
- For a meromorphic function f(z), any point a for which f(z)→∞ as z→a.
- A unit of length, equal to a rod (¹⁄₄ chain or 5+¹⁄₂ yards).
- A penis.
- A contact on an electrical device (such as a battery) at which electric current enters or leaves.
verb
- To propel by pushing with poles, to push with a pole.
- To furnish with poles for support.
- To identify something quite precisely using a telescope.
- To convey on poles.
- To stir, as molten glass, with a pole.
- To strike (the ball) very hard.
- To induce piezoelectricity in (a substance) by aligning the dipoles.
noun
- A point in a convex set which does not lie in any open line segment joining two points in the set.
- A leaf vertex of a tree data structure.
- The maximum or minimum of a function.
- A standpoint that goes farthest in some dimension or on some criterion.
- A point that is physically located farthest in the direction of the edge of something.
noun
- (of a set) The set of points in the closure of a set S, not belonging to the interior of that set.
- An edge or line marking an edge of the playing field.
- The bounds, confines, or limits between immaterial things (such as one’s comfort zone, privacy, or professional sphere and the realm beyond).
- The dividing line or location between two areas.
- An event whereby the ball is struck and either touches or passes over a boundary (with or without bouncing), usually resulting in an award of 4 (four) or 6 (six) runs respectively for the batting team.
noun
- A number in intersection theory. A positive-dimensional variety sometimes behaves formally as if it were a finite number of points; this number is its equivalence.
- The quantity of the combining power of an atom, expressed in hydrogen units; the number of hydrogen atoms can combine with, or be exchanged for; valency.
- An equivalence relation; ≡; ~
- A Boolean operation that is TRUE when both input variables are TRUE or both input variables are FALSE, but otherwise FALSE; the XNOR function.
- The condition of being equivalent or essentially equal.
- The relationship between two propositions that are either both true or both false.
- The degree to which a term or text in one language is semantically similar to its translated counterpart.
verb
noun
- The topology of a Euclidean space ℝⁿ such that any subset of that space is open (i.e. belonging to the topology) if it can be written as a union of open balls from that space.
- The topology of the real number system generated by a basis which consists of all open balls (in the real number system), which are defined in terms of the one-dimensional Euclidean metric.
noun
- A monoid object in the category of endofunctors of a fixed category.
- A single individual (such as a pollen grain) that is free from others, not united in a group.
- A data type which represents a specific form of computation, along with the operations "return" and "bind".
- An ultimate atom, or simple, unextended point; something ultimate and indivisible.
noun
- The smallest set that possesses a particular property (such as convexity) and contains every point of A; slightly more formally, the intersection of all sets which possess the specified property and of which A is a subset.
- The outer covering of a fruit or seed.
- Any covering.
- The body or frame of a vessel, such as a ship or plane.
verb
verb
- spread out or open from a closed or folded state
- cause to open or to become open
- start to operate or function or cause to start operating or functioning
- become open
- begin or set in action, of meetings, speeches, recitals, etc.
- make available
- become available
- have an opening or passage or outlet
- make the opening move
- afford access to
- display the contents of a file or start an application as on a computer
adj
- with no protection or shield
- open to or in view of all
- not having been filled
- accessible to all
- not defended or capable of being defended
- (of textures) full of small openings or gaps
- having no protecting cover or enclosure
- not brought to a conclusion; subject to further thought
- not sealed or having been unsealed
- without undue constriction as from e.g. tenseness or inhibition
- not requiring union membership
- possibly accepting or permitting
- affording free passage or view
- openly straightforward and direct without reserve or secretiveness
- ready for business
noun
- a clear or unobstructed space or expanse of land or water
- where the air is unconfined
- a tournament in which both professionals and amateurs may play
- information that has become public
adj
verb
- spread out or open from a closed or folded state
- distribute or disperse widely
- become distributed or widespread
- spread across or over
- cause to become widely known
- become widely known and passed on
- strew or distribute over an area
- move outward
- cover by spreading something over
- distribute over a surface in a layer
noun
- process or result of distributing or extending over a wide expanse of space
- a conspicuous disparity or difference as between two figures
- farm consisting of a large tract of land along with facilities needed to raise livestock (especially cattle)
- a haphazard distribution in all directions
- a tasty mixture to be spread on bread or crackers or used in preparing other dishes
- a meal that is well prepared and greatly enjoyed
- two facing pages of a book or other publication
- the expansion of a person's girth (especially at middle age)
- decorative cover for a bed
- act of extending over a wider scope or expanse of space or time
adj
noun
noun
- A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
- A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.
- An algebraic structure consisting of a module over a commutative ring (or a vector space over a field) along with an additional binary operation that is bilinear over module (or vector) addition and scalar multiplication.
- A universal algebra.
- One of several other types of mathematical structure.
- The study of algebraic structures.
- The surgical treatment of a dislocated or fractured bone. Also (countable): a dislocation or fracture.
- A system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
verb
- Of sets: to have some elements in common.
- To have an area, range, character or function in common.
- To have some similar nucleotide sequences.
- To extend over and partly cover something.
noun
- Something that overlaps or is overlapped
- a situation in the game where an attacking line has more players in it than the defensive line coming to meet it. The attacking side may exploit the overlap by using their superior numbers to break the opposition's defensive line. If attackers outnumber defenders by more than one player this is often termed a two man overlap or three man overlap, etc. If the attacking side fails to break through usually due to poor execution, they are said to waste an overlap.
- The payment of a spouse's or other dependant's annuity benefits concurrently with the member's benefits, on death of the member during the guarantee period.
noun
- A non-self-intersecting closed curve in (e.g., three-dimensional) space that is an abstraction of a knot (in sense 1 above).
- A maze-like pattern.
- A looping of a piece of string or of any other long, flexible material that cannot be untangled without passing one or both ends of the material through its loops.
- A tangled clump.
- Any knob, lump, swelling, or protuberance.
- A kind of epaulet; a shoulder knot.
- One of a variety of shore birds; red-breasted sandpiper (variously Calidris canutus or Tringa canutus).
- A bond of union; a connection; a tie.
- A unit of speed, equal to one nautical mile per hour. (From the practice of counting the number of knots in the log-line (as it is paid out) in a standard time. Traditionally spaced at one every ¹⁄₁₂₀ of a mile.)
- Local swelling in a tissue area, especially skin, often due to injury.
- The bulbus glandis.
- The whorl left in lumber by the base of a branch growing out of the tree's trunk.
- A difficult situation.
- A tightened and contracted part of a muscle that feels like a hard lump under the skin.
- A node.
- A group of people or things.
- A unit of indicated airspeed, calibrated airspeed, or equivalent airspeed, which varies in its relation to the unit of speed so as to compensate for the effects of different ambient atmospheric conditions on aircraft performance.
- In omegaverse fiction, a bulbus glandis-like structure on the penis of a male alpha, which ties him to an omega during intercourse.
- A nautical mile.
- The point on which the action of a story depends; the gist of a matter.
- A protuberant joint in a plant.
- The swelling of the bulbus glandis in members of the dog family, Canidae.
verb
English words for 'A topology in which the intersection of any family of open sets is an open set.'
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