continuous
holomorphic
semiregular
Lindelöf covering theorem
neighborhood
continuous function
T₁
generic property
compact
empty function
inclusion function
directed
paracompact
measurable function
regular
embed
quotient map
regular space
Hintikka set
Borel measurable
germ
quasi-compact
open
overt
metacompact
sheaf
pretopology
Alexandrov topology
flabby
paracontact
hyperconnected
Kolmogorov
Lindelöf space
avowedly
preimage
normal space
nonvanishing
ball
single-valued function
professedly
Grothendieck topology
restrict
choice function
little v
open set
set
lectically
sets
characteristic function
surjection
totally disconnected
indicator function
set theoretically
ultradifferentiable
domain
tier
Lp space
netted
codomain
Cantor-Bendixson theorem
weblike
netlike
lacy
dual
webby
layer
webbed
standard topology
kernel
valuation
support
wide-open
smooth
sumti
unfold
macrodomain
fixed point
axiom of pairing
non-empty
many-to-many
Kolmogorov space
Baire space
Kripke frame
lake of Wada
tetradomain
Tarski-Seidenberg theorem
quasimeasure
Grothendieck universe
identity
algebraic structure
omnibearing
quasilocal
patulous
discrete topology
sphere
local
continuous
holomorphic
semiregular
T₁
compact
directed
paracompact
regular
Borel measurable
quasi-compact
open
overt
metacompact
flabby
hyperconnected
Kolmogorov
nonvanishing
totally disconnected
ultradifferentiable
netted
weblike
netlike
lacy
dual
webby
webbed
wide-open
smooth
fixed point
non-empty
many-to-many
tetradomain
omnibearing
quasilocal
patulous
local
avowedly
professedly
lectically
set theoretically
neighborhood
continuous function
generic property
empty function
inclusion function
measurable function
quotient map
regular space
Hintikka set
germ
sheaf
pretopology
Alexandrov topology
paracontact
Lindelöf space
preimage
normal space
ball
single-valued function
Grothendieck topology
choice function
little v
open set
set
sets
characteristic function
surjection
indicator function
domain
Lp space
codomain
standard topology
kernel
valuation
support
sumti
macrodomain
axiom of pairing
Kolmogorov space
Baire space
Kripke frame
lake of Wada
quasimeasure
Grothendieck universe
identity
algebraic structure
discrete topology
sphere
embed
restrict
tier
layer
unfold
adj
- Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).
- 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.
- Expressing an ongoing action or state.
- Not deviating or varying from uniformity; not interrupted; not joined or articulated.
- Without stopping; without a break, cessation, or interruption.
- Without intervening space; continued.
noun
- Alternatively: An open set which contains some specified point.
- A set containing an open set which contains some specified point.
- 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.
- 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.
- An approximate amount.
- The quality of physical proximity.
- Alternatively: An open ball which contains some specified point.
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
- 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.
verb
- To form an agreement or contract.
- To make more dense; to compress.
- To unite or connect firmly, as in a system.
noun
adj
- Such that every set in its domain is both outer regular and inner regular.
- Having the expected characteristics or appearances; normal, ordinary, standard.
- Having all the parts of the same kind alike in size and shape.
- Bound by religious rule; belonging to a monastic or religious order (often as opposed to secular).
- Demonstrating a consistent set of rules; showing order, evenness of operation or occurrence.
- Exemplary; excellent example of; utter, downright.
- Happening at constant (especially short) intervals.
- Permanently organised; being part of a set professional body of troops.
- Having bowel movements or menstrual periods at constant intervals in the expected way.
- Riding with the left foot forward.
- Isometric.
- Both equilateral and equiangular; having all sides of the same length, and all (corresponding) angles of the same size
- Whose faces are all congruent regular polygons, equally inclined to each other.
- Following a set or common pattern; according to the normal rules of a given language.
- Having a constant pattern; showing evenness of form or appearance.
- Of a moon or other satellite: following a relatively close and prograde orbit with little inclination or eccentricity.
noun
- A member of a religious order who has taken the three ordinary vows.
- A frequent, routine visitor to an establishment.
- A member of an armed forces or police force.
- A frequent customer, client or business partner.
- A number for each year, giving, added to the concurrents, the number of the day of the week on which the Paschal full moon falls.
- A coffee with one cream and one sugar.
- A fixed number for each month serving to ascertain the day of the week, or the age of the moon, on the first day of any month.
- A member of the British Army (as opposed to a member of the Territorial Army or Reserve).
- Anything that is normal or standard.
verb
- To define a one-to-one function from one set to another so that certain properties of the domain are preserved when considering the image as a subset of the codomain.
- To encapsulate within another document or data file.
- To lay (something) as in a bed; to lay in surrounding matter; to bed.
- To include (something) in surrounding matter.
noun
- An element of an advertisement, etc. serving as a subliminal message.
- An embedded reporter or journalist, such as a war reporter assigned to and travelling with a military unit, or a political reporter assigned to follow and report on the campaign of a candidate.
- An item embedded in another document.
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
adj
- open and observable; not secret or hidden
- 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
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
- 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
verb
- 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.
- spread out or open from a closed or folded state
- 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
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
- Of an expression, especially a function, being nonzero at a value, everywhere on a specified set, or on the entire domain.
- where a 𝜎₂ is holomorphic and nonvanishing at 0.
- {{quote-book|en
- 𝜎₁(𝜆) holomorphic and nonvanishing at 0,
- This means that the vector space of solutions of (2.25) near 𝜆=0 is generated by
- 2013-11-11, C. Herbert Clemens, A Scrapbook of Complex Curve Theory (University Series in Mathematics), Springer Science & Business Media, →ISBN, →OCLC, page 61
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 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
- Set theory.
- A punch for setting nails in wood.
- The full number of eggs set under a hen.
- The initial or basic formation of dancers.
- A device for receiving broadcast radio waves (or, more recently, broadcast data); a radio or television.
- A young oyster when first attached.
- The act of directing the ball to a teammate for an attack.
- The setting of the sun or other luminary; (by extension) the close of the day.
- The scenery for a film or play.
- the general locations and area where a movie’s, a film’s, or a video’s scenery is arranged to be filmed also including places for actors, assorted crew, director, producers which are typically not filmed.
- A complete series of games, forming part of a match.
- A group of repetitions of a single exercise performed one after the other without rest.
- The amount the teeth of a saw protrude to the side in order to create the kerf.
- A rudimentary fruit.
- An object made up of several parts.
- General movement; direction; drift; tendency.
- A piece placed temporarily upon the head of a pile when the latter cannot otherwise be reached by the weight, or hammer.
- The camber of a curved roofing tile.
- A drum kit, a drum set.
- A class group in a subject where pupils are divided by ability.
- A bias of mind; an attitude or pattern of behaviour.
- A collection of zero or more objects, possibly infinite in size, and disregarding any order or repetition of the objects which may be contained within it.
- A musical performance by a band, disc jockey, etc., consisting of several musical pieces.
- Three of a kind, especially if two cards are in one's hand and the third is on the board. Compare trips (“three of a kind, especially with two cards on the board and one in one's hand”).
- A young plant fit for setting out; a slip; shoot.
- A small tuber or bulb used instead of seed, particularly onion sets and potato sets.
- Collectively, the crop of young oysters in any locality.
- A series or group of something. (Note the similar meaning in Etymology 4, Noun)
- A group of people, usually meeting socially.
- The manner, state, or quality of setting or fitting; fit.
- The pattern of a tartan, etc.
- A collection of various objects for a particular purpose.
- A permanent change of shape caused by excessive strain, as from compression, tension, bending, twisting, etc.
- A matching collection of similar things. (Note the similar meaning in Etymology 2, Noun.)
- A complete series of points, forming part of a match.
adj
- Fixed in one’s opinion.
- Fixed in a certain style.
- Ready, prepared.
- Rigid, solidified.
- Prearranged.
- Fixed in position.
- Intent, determined (to do something).
verb
- To devise and assign (work) to.
- To have a certain direction of motion; to flow; to move on; to tend.
- To arrange with dishes and cutlery, to set the table.
- To direct (the ball) to a teammate for an attack.
- To place or fix in a setting.
- To extend and bring into position; to spread.
- To place plants or shoots in the ground; to plant.
- To prepare (a stage or film set).
- To lower into place and fix solidly, as the blocks of cut stone in a structure.
- To defeat a contract.
- To become fixed or rigid; to be fastened.
- To put (something) down, to rest.
- To produce after pollination.
- To render stiff or solid; especially, to convert into curd; to curdle.
- To acknowledge a dancing partner by facing him or her and moving first to one side and then to the other, while she or he does the opposite.
- To give a pitch to, as a tune; to start by fixing the keynote.
- To reduce from a dislocated or fractured state.
- To put in order in a particular manner; to prepare.
- To punch (a nail) into wood so that its head is below the surface.
- To hunt game with the aid of a setter.
- To sit (be in a seated position).
- To arrange (type).
- To be fixed for growth; to strike root; to begin to germinate or form.
- To introduce or describe.
- To solidify.
- To rest or lie somewhere, on something, etc.; to occupy a certain place.
- To apply oneself; to undertake earnestly.
- Of a heavenly body, to disappear below the horizon of a planet, etc, as the latter rotates.
- Of a dog, to indicate the position of game.
- To fit (someone) up in a situation.
- To put in a specified condition or state; to cause to be.
- To adjust.
- To compile, to make (a puzzle or challenge).
- To suit; to become.
- To establish as a rule; to furnish; to prescribe; to assign.
- To determine or settle.
- To fit music to words.
- To adorn with something infixed or affixed; to stud; to variegate with objects placed here and there.
- To start (a fire).
- To divide a class group in a subject according to ability
- To locate (a play, etc.); to assign a backdrop to, geographically or temporally.
- To attach or affix (something) to something else, or in or upon a certain place.
noun
noun
- An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.
- 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.
- The set of all possible mathematical entities (points) where a given function is defined.
- Any DNS domain name, particularly one which has been delegated and has become representative of the delegated domain name and its subdomains.
adj
- Being the space of all linear functionals of (some other space).
- Characterized by having two (usually equivalent) components.
- Pertaining to a grammatical number in certain languages that refers to two of something, such as a pair of shoes.
- Exhibiting duality.
- Being the dual of some other category; containing the same objects but with source and target reversed for all morphisms.
- Pertaining to two, pertaining to a pair of.
verb
noun
- Of a vector in an inner product space, the linear functional corresponding to taking the inner product with that vector. The set of all duals is a vector space called the dual space.
- The dual number.
- Of an item that is one of a pair, the other item in the pair.
- Of a regular polyhedron with V vertices and F faces, the regular polyhedron having F vertices and V faces.
verb
noun
- One of the items in a hierarchy.
- A person who lays anything, such as tiles or a wager.
- A (usually) horizontal deposit; a stratum.
- A shoot of a plant, laid underground for growth.
- An item of clothing worn under or over another.
- A single thickness of some material covering a surface.
- A mature female bird, insect, etc. that is able to lay eggs.
- A hen kept to lay eggs.
- one in a stack of (initially transparent) drawing surfaces that comprise an image; used to keep elements of an image separate so that they can be modified independently from one another.
noun
- 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.
- 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.
noun
- For a given function (especially a linear map between vector spaces), the set of elements in the domain which are mapped to zero; (formally) given f : X → Y, the set {x ∈ X : f(x) = 0}.
- A set of pairs of a mapping's domain which are mapped to the same value.
- The human clitoris.
- The nucleus and electrons of an atom excluding its valence electrons.
- For a category with zero morphisms: the equalizer of a given morphism and the zero morphism which is parallel to that given morphism.
- A single seed or grain, especially of corn or wheat.
- A small mass around which other matter is concreted; a nucleus; a concretion or hard lump in the flesh.
- The set of members of a fuzzy set that are fully included (i.e., whose grade of membership is 1).
- The core, center, or essence of an object or system.
- The central part of many computer operating systems which manages the system's resources and the communication between hardware and software components.
- The stone of certain fruits, such as peaches or plums.
- A function used to define an integral transform.
- The core engine of any complex software system.
- The central (usually edible) part of a nut, especially once the hard shell has been removed.
verb
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
- in relation to a function, the set of points where the function is not zero, or the closure of that set.
- An actor playing a subordinate part with a star.
- Answers to questions and resolution of problems regarding something sold.
- Evidence.
- Something which supports.
- An accompaniment in music.
- Compatibility and functionality for a given product or feature.
- Horizontal, vertical or rotational support of structures: movable, hinged, fixed.
- Financial or other help.
- A set whose elements are at least partially included in a given fuzzy set (i.e., whose grade of membership in that fuzzy set is strictly greater than zero).
verb
- To keep from falling.
- To be designed (said of machinery, electronics, or computers, or their parts, accessories, peripherals, or programming) to function compatibly with or provide the capacity for.
- To help, particularly financially.
- To back a cause, party, etc., mentally or with concrete aid.
- To serve, as in a customer-oriented mindset; to give support to.
- To verify; to make good; to substantiate; to establish; to sustain.
- To answer questions and resolve problems regarding something sold.
- To be accountable for, or involved with, but not responsible for.
- To assume and carry successfully, as the part of an actor; to represent or act; to sustain.
adj
- Having derivatives of all finite orders at all points within the function’s domain.
- Flowing or uttered without check, obstruction, or hesitation; not harsh; fluent.
- Natural; unconstrained.
- Not grainy; having an even texture.
- Without difficulty, problems, or unexpected consequences or incidents.
- Involuntary and non-striated.
- That factors completely into small prime numbers.
- Having a texture that lacks friction. Not rough.
- Unbroken.
- Lacking marked aspiration.
- Lacking projections or indentations; not serrated.
- Placid, calm.
- Having a pleasantly rounded flavor; neither rough nor astringent.
- Suave; sophisticated.
- Bland; glib.
noun
- The analysis obtained through a smoothing procedure.
- Something that is smooth, or that goes smoothly and easily.
- A domestic animal having a smooth coat.
- A member of an anti-hippie fashion movement in 1970s Britain.
- A smoothing action.
verb
- To make smooth or even.
- To make straightforward or easy.
- To stroke; especially to stroke an animal's fur.
- To reduce to a particular shape or form by pressure; to press, to flatten.
- To calm or palliate.
- To capture important patterns in the data, while leaving out noise.
adv
noun
noun
- Any function which maps all elements of its domain to themselves.
- An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.
- A well-known or famous person.
- A name or persona—a mask or appearance one presents to the world—by which one is known.
- The difference or character that marks off an individual or collective from the rest of the same kind; selfhood; the sense of who something or someone or oneself is, or the recurring characteristics that enable the recognition of such an individual or group by others or themself.
- An equation which always holds true regardless of the choice of input variables.
- Sameness, identicalness; the quality or fact of (several specified things) being the same.
noun
- a mathematical object comprising a carrier set (aka underlying set or domain), an optional scalar set, a set of operations (typically binary operations, but otherwise each of finite arity) and a set of identities (axioms) which the operations must satisfy.
- Any one of the numerous types of mathematical object studied in algebra and especially in universal algebra;
noun
- The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .
- The region in which something or someone is active; one's province, domain.
- A regular three-dimensional object in which every cross-section is a circle; the figure described by the revolution of a circle about its diameter .
- A spherical physical object; a globe or ball.
- Any of the concentric hollow transparent globes formerly believed to rotate around the Earth, and which carried the heavenly bodies; there were originally believed to be eight, and later nine and ten; friction between them was thought to cause a harmonious sound (the music of the spheres).
- The extension of a general conception, or the totality of the individuals or species to which it may be applied.
- An area of activity for a planet; or by extension, an area of influence for a god, hero etc.
verb
adj
- Applying to each point in a space rather than the space as a whole.
- Holonyms: statal, national, federal, unional, supranational, global
- Of or pertaining to a restricted part of an organism.
- Connected directly to a particular computer, processor, etc.; able to be accessed offline.
- From or in a nearby location.
- Having limited scope (either lexical or dynamic); only being accessible within a certain portion of a program.
- Descended from an indigenous population.
adv
noun
- A Twitter user who is not a part of Stan Twitter.
- One's nearest or regularly frequented public house or bar.
- An independent trader who acts for themselves rather than on behalf of investors.
- A person who lives near a given place.
- A locally scoped identifier.
- An item of news relating to the place where the newspaper is published.
- A branch of a nationwide organization such as a trade union.
English words for 'Such that each open set in the target space has an open preimage (in the domain space, with respect to the given function).'
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