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1. Category of topological spaces: In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again continuous, and the ... [100%] 2023-12-21 [Categories in category theory] [General topology]...
2. Axiomatic foundations of topological spaces: In the mathematical field of topology, a topological space is usually defined by declaring its open sets.({{{1}}}, {{{2}}}) However, this is not necessary, as there are many equivalent axiomatic foundations, each leading to exactly the same concept. For instance ... [89%] 2023-11-08 [General topology]
3. Axiomatic foundations of topological spaces: In the mathematical field of topology, a topological space is usually defined by declaring its open sets. However, this is not necessary, as there are many equivalent axiomatic foundations, each leading to exactly the same concept. [89%] 2024-10-05 [Categories in category theory] [General topology]...
4. Characterizations of the category of topological spaces: In mathematics, a topological space is usually defined in terms of open sets. However, there are many equivalent characterizations of the category of topological spaces. [75%] 2023-10-31 [General topology]

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1. Topological space: A topological space is a pair (X, T), where X is a set, and T is a collection of subsets of X that satisfy the following 3 axioms: Elements in T are called "open sets". [100%] 2023-06-28 [Topology]
2. Topological space: A totality of two elements: A set $X$, consisting of elements of an arbitrary nature, called points of the given space, and a topological structure, or topology, on this set $X$ (cf. Topological structure (topology)); it is immaterial whether this ... (Mathematics) [100%] 2023-10-25
3. Topological space: In mathematics, a topological space is an ordered pair ( X , T ) {\displaystyle (X,{\mathcal {T}})} where X {\displaystyle X} is a set and T {\displaystyle {\mathcal {T}}} is a certain collection of subsets of X {\displaystyle X} called the open ... [100%] 2023-06-30
4. Topological space: In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with ... (Mathematical space with a notion of closeness) [100%] 2024-01-12 [General topology] [Topological spaces]...
5. Topological vector space: In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is ... (Vector space with a notion of nearness) [81%] 2023-12-28 [Articles containing proofs] [Topology of function spaces]...
6. Noetherian topological space: In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the ... [81%] 2024-01-12 [Algebraic geometry] [Properties of topological spaces]...
7. Topological vector space: over a topological field $ K $ A vector space $ E $ over $ K $ equipped with a topology (cf. Topological structure (topology)) that is compatible with the vector space structure, that is, the following axioms are satisfied: 1) the mapping $ ( x _ {1 ... (Mathematics) [81%] 2023-10-18
8. Pre-topological space: Let $X$ be a set and $\mathcal{P}X$ the set of subsets of $X$. A pre-topological space structure on $X$ is defined by a Čech closure operator, a mapping $C : \mathcal{P}X \rightarrow \mathcal{P}X$ such ... (Mathematics) [81%] 2023-11-14
9. Irreducible topological space: hyperconnected A topological space that cannot be represented as the union of two proper closed subspaces. Equivalently, an irreducible topological space can also be defined by postulating that any open subset of it is connected or that any non-empty ... (Mathematics) [81%] 2023-10-23 [General topology]
10. Topological vector space: In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is ... (Vector space with a notion of nearness) [81%] 2024-01-12 [Articles containing proofs] [Topology of function spaces]...
11. Finite topological space: In mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space which has only finitely many elements. [81%] 2023-11-23 [Topological spaces] [Combinatorics]...
12. Finite topological space: In mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space which has only finitely many elements. [81%] 2024-09-09 [Topological spaces] [Combinatorics]...
13. Topologically stratified space: In topology, a branch of mathematics, a topologically stratified space is a space X that has been decomposed into pieces called strata; these strata are manifolds and are required to fit together in a certain way. Topologically stratified spaces provide ... [72%] 2023-10-29 [Singularity theory] [Generalized manifolds]...
14. Space of mappings, topological: A set $F$ of mappings from a set $X$ into a topological space $Y$ with some natural topology $\mathfrak{T}$ on $F$. For fixed $X$ and $Y$ one obtains different spaces of mappings, depending on which mappings $X \rightarrow Y ... (Mathematics) [70%] 2023-12-22
15. Complete topological vector space: In functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point \displaystyle{ x }[/math] towards ... (A TVS where points that get progressively closer to each other will always converge to a point) [70%] 2023-12-03 [Functional analysis] [Topological vector spaces]...
16. Complete topological vector space: In functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point x {\displaystyle x} towards ... (A TVS where points that get progressively closer to each other will always converge to a point) [70%] 2021-12-22 [Topological vector spaces]
17. Metrizable topological vector space: In functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. (A topological vector space whose topology can be defined by a metric) [70%] 2021-12-21 [Topological vector spaces]
18. Ordered topological vector space: In mathematics, specifically in functional analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial order ≤ making it into an ordered vector space whose positive ... [70%] 2024-03-21 [Functional analysis] [Order theory]...
19. Topologika: Topologika Software Ltd was an independent United Kingdom publisher of educational software. Established in Stilton, Cambridgeshire in 1983, the company spent most of its life in Penryn, Cornwall before moving to Brighton, Sussex. (Company) [70%] 2023-11-10 [Educational software companies]