hyperconnected
normal space
Alexandrov topology
T₁
disjoint
compact
Baire space
regular space
connected
prevariety
ring
angelic
symmetric difference
Hintikka set
filter
Lindelöf covering theorem
complement
open set
sheaf
cofinite topology
Cantor-Bendixson theorem
cardinal number
quasi-compact
discrete
generic property
absolute complement
σ-compact
paracompact
agape
gaping
inhomogeneous
agog
nonuniform
nonhomogeneous
semiregular
wide-open
yawning
unfold
spread out
lake of Wada
disjoint set
open
spread
wild
disconnected
group
mathematical group
neighborhood
axiom of union
disjoint union
Hausdorff space
hyperconnection
infinitive
continuous function
partition
pseudointersection
σ-finite measure
diffuse
nonempty
quintuplicate
separating
connected space
gape
π-system
dishomogeneous
precompact
unhomogeneous
connection
hyperbolic geometry
apeirotope
principal ultrafilter
sober space
broad
solvmanifold
metacompact
superprojective
perfect set
Russell's paradox
ball
algebra
torsor
continuous
gapingly
topology
Murasugi sum
proper subset
various
setwise
assorted
mode
amorphous
domatic
axiom of pairing
pectinate
coinvariant
hyperconnected
T₁
disjoint
compact
connected
angelic
quasi-compact
discrete
σ-compact
paracompact
agape
gaping
inhomogeneous
agog
nonuniform
nonhomogeneous
semiregular
wide-open
yawning
wild
disconnected
infinitive
diffuse
nonempty
separating
dishomogeneous
precompact
unhomogeneous
broad
metacompact
superprojective
continuous
various
setwise
assorted
amorphous
domatic
pectinate
coinvariant
agape
gapingly
normal space
Alexandrov topology
Baire space
regular space
prevariety
ring
symmetric difference
Hintikka set
filter
complement
open set
sheaf
cofinite topology
cardinal number
generic property
absolute complement
lake of Wada
disjoint set
group
mathematical group
neighborhood
axiom of union
disjoint union
Hausdorff space
hyperconnection
continuous function
partition
pseudointersection
σ-finite measure
quintuplicate
connected space
gape
π-system
connection
hyperbolic geometry
apeirotope
principal ultrafilter
sober space
solvmanifold
perfect set
ball
algebra
torsor
topology
Murasugi sum
proper subset
mode
axiom of pairing
unfold
spread out
open
spread
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
- That cannot be partitioned into two nonempty open sets.
- Having a path, either directed or undirected, connecting every pair of vertices.
- Having favorable rapport with a powerful entity.
- Intimate; Having bonds of affection.
- Involved with organized crime, specifically someone not (yet) working for a crime organization, but referred to as a "friend" by made guys/wise guys inside the organization.
- Having or supporting connections, especially when through technology such as networking software or a transportation network.
- Having relationships; involved with others.
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.
adj
- A regular Hausdorff space is said to be angelic if the closure of each relatively countably compact set A is compact and the closure consists of the limits of sequences in A.
- Belonging to, or proceeding from, angels; resembling, characteristic of, or partaking of the nature of, an angel.
- Very sweet-natured or well-behaved.
- Of or pertaining to angelic acid.
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
- Given two sets, the set containing one set's elements that are not members of the other set (whether a relative complement or an absolute complement).
- Fullness (of the moon).
- A nucleotide sequence in which each base is replaced by the complementary base of the given sequence: adenine (A) by thymine (T) or uracil (U), cytosine (C) by guanine (G), and vice versa.
- An angle which, together with a given angle, makes a right angle.
- Something which completes, something which combines with something else to make up a complete whole; loosely, something perceived to be a harmonious or desirable partner or addition.
- A word or group of words that completes a grammatical construction in the predicate and that describes or is identified with the subject or object.
- A voltage level with the opposite logical sense to the given one.
- A bit with the opposite value to the given one; the logical complement of a number.
- One of several blood proteins that work with antibodies during an immune response.
- Obsolete spelling or misspelling of compliment.
- The radix complement of a number; the two's complement of a binary number.
- The whole working force of a vessel.
- An interval which, together with the given interval, makes an octave.
- The diminished radix complement of a number; the nines' complement of a decimal number; the ones' complement of a binary number.
- The numeric complement of a number.
- Synonym of alexin
- An expression related to some other expression such that it is true under the same conditions that make other false, and vice versa.
- The color which, when mixed with the given color, gives black (for mixing pigments) or white (for mixing light).
- The totality, the full amount or number which completes something.
verb
noun
- A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set.
- Most generally, a member of the topology of a given topological space.
- Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.
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
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 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.
adj
adj
adj
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
- affording unobstructed entrance and exit; not shut or closed
- affording free passage or access
- used of mouth or eyes
- (set theory) of an interval that contains neither of its endpoints
- ready or willing to receive favorably
- open and observable; not secret or hidden
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
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
adj
- Not capable of being represented as a finite closed polygonal chain.
- From or relating to wild creatures.
- Disheveled, tangled, or untidy.
- Hard to steer.
- Raucous, unruly, or licentious.
- Furious; very angry.
- Exposed to the wind and sea; unsheltered.
- Amazing, awesome, unbelievable.
- Untamed; not domesticated; specifically, in an unbroken line of undomesticated animals (as opposed to feral, referring to undomesticated animals whose ancestors were domesticated).
- Of an audio recording: intended to be synchronized with film or video but recorded separately.
- Enthusiastic.
- Of unregulated and varying frequency.
- Able to stand in for others, e.g. a card in games, or a text character in computer pattern matching.
- Unrestrained or uninhibited.
- Visibly and overtly anxious; frantic.
- Very inaccurate; far off the mark.
noun
- The undomesticated state of a wild animal.
- A wilderness.
- civilization at large as opposed to contrived or laboratory conditions.
adv
- Intended to be synchronized with film or video but recorded separately.
- Inaccurately; not on target.
verb
noun
- Alternatively: An open set which contains some specified 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.
- The infinitesimal open set of all points that may be reached directly from a given point.
- An approximate amount.
- The quality of physical proximity.
- Alternatively: An open ball which contains some specified point.
noun
- A union of sets which are already pairwise disjoint.
- A union of sets forced to be disjoint by attaching information referring to the original sets to their elements (i.e., by using indexing).
- The disjoint union of the underlying sets of a given family of topological spaces, equipped with a topology.
adj
noun
- A non-finite verb form considered neutral with respect to inflection; depending on language variously found used with auxiliary verbs, in subordinate clauses, or acting as a gerund, and often as the dictionary form.
- The infinitive mood or mode (a grammatical mood).
- A verbal noun formed from the infinitive of a verb.
noun
- A collection of non-empty, disjoint subsets of a set whose union is the set itself (i.e. all elements of the set are contained in exactly one of the subsets).
- A vertical structure that divides a room.
- An approach to division in which one asks what the size of each part is, rather than (as in quotition) how many parts there are.
- A musical score.
- An action which divides a thing into parts, or separates one thing from another.
- A part of something that has been divided.
- A part divided off by walls; an apartment; a compartment.
- That which divides or separates; that by which different things, or distinct parts of the same thing, are separated; boundary; dividing line or space.
- The severance of common or undivided interests, particularly in real estate. It may be effected by consent of parties, or by compulsion of law.
- The division of a territory into two or more autonomous ones.
- A division of a database or one of its constituting elements such as tables into separate independent parts.
- A section of a hard disk separately formatted.
verb
noun
- The width of an opening.
- An act of gaping; a yawn.
- A disease in poultry caused by gapeworm in the windpipe, a symptom of which is frequent gaping.
- A large opening.
- The maximum opening of the mouth (of a bird, fish, etc.) when it is open.
verb
- To open wide; to display a gap.
- To open the passage to the vomeronasal organ, analogous to the flehming in other animals.
- To depict a dilated anal or vaginal cavity upon penetrative sexual activity.
- To stare in wonder.
- To open the mouth wide, especially involuntarily, as in a yawn, anger, or surprise.
adj
adj
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.
adj
- Extended, in the sense of diffused; open; clear; full.
- General rather than specific.
- Comprehensive; liberal; enlarged.
- Having a large measure of any thing or quality; unlimited; unrestrained.
- Unsubtle; obvious.
- Plain; evident.
- Free; unrestrained; unconfined.
- Strongly regional.
- Wide in extent or scope.
- Velarized, i.e. not palatalized.
noun
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
- 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.
adj
- Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).
- Expressing an ongoing action or state.
- Not deviating or varying from uniformity; not interrupted; not joined or articulated.
- Such that, for every x in the domain, for each small open interval D about f(x), there's an interval containing x whose image is in D.
- Without stopping; without a break, cessation, or interruption.
- Without intervening space; continued.
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.
noun
- The union of a finite sequence of surfaces taken over a disk common to every adjacent pair of the sequence, such that the boundary of the disk comprises some even number of closed arcs, disjoint except at their endpoints, which are alternatingly subarcs of the two surfaces' boundaries.
- The union of links formed by taking such a sum of their Seifert surfaces and taking the boundary of the result.
noun
- The openwork between the solid parts of a pattern.
- A series of settings on a device used for a specific purpose.
- A verb form that depends on how its containing clause relates to the speaker’s or writer’s wish, intent, or assertion about reality.
- The most frequently occurring value in a distribution
- A variation in gameplay, such as a difficulty level.
- One of several common scales in modern Western music, one of which corresponds to the modern major scale and one to the natural minor scale.
- Style or fashion; popular trend.
- That which exists only as a quality of substance.
- One of various related sets of rules for processing data; more generally, any state of the system associated with certain behaviours.
- A particular means of accomplishing something.
- One of several ancient Greek scales.
- A particular state of being, or frame of mind.
- A state of a system that is represented by an eigenfunction of that system.
- In lace-making, a small decorative piece inserted into a pattern.
English words for 'That is not the union of two proper closed sets; such that every open set is dense.'
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