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1. Topological structure (topology): open topology, respectively, closed topology A collection $\mathfrak G$, respectively $\mathfrak F$, of subsets of a set $X$, satisfying the following properties: $1$. The set $X$, as well as the empty set $\emptyset$, are elements of the collection $\mathfrak G ... (Topology) [100%] 2023-09-10 [General topology]
2. Topological structures: General topology (also called set-theoretic topology or analytic topology, cf. Topology, general) tries to explain such concepts as convergence and continuity known from classical analysis in a general setting. (Mathematics) [94%] 2023-10-17
3. 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". [84%] 2023-06-28 [Topology]
4. 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) [84%] 2023-10-25
5. 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 ... [84%] 2023-06-30
6. 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) [84%] 2024-01-12 [General topology] [Topological spaces]...
7. Structure space: of a ring $R$ The set $\mathfrak P$ of all primitive ideals $R$ with the following topology: A subset $C\subseteq\mathfrak P$ is closed if $C$ contains every ideal that contains the intersection of all ideals from $C$ (see ... (Mathematics) [79%] 2023-10-26
8. 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) [68%] 2023-12-28 [Articles containing proofs] [Topology of function spaces]...
9. 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 ... [68%] 2024-01-12 [Algebraic geometry] [Properties of topological spaces]...
10. 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) [68%] 2023-10-18
11. 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) [68%] 2023-11-14
12. 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) [68%] 2023-10-23 [General topology]
13. 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) [68%] 2024-01-12 [Articles containing proofs] [Topology of function spaces]...
14. 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. [68%] 2023-11-23 [Topological spaces] [Combinatorics]...
15. 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. [68%] 2024-09-09 [Topological spaces] [Combinatorics]...
16. Structure: A synonym for algebraic system. Similarly, substructure is a synonym for "subsystem" , and elementary substructure is a synonym for "elementary subsystem" (cf. (Mathematics) [67%] 2023-10-17
17. Structure: A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as biological ... (Arrangement of interrelated elements in an object/system, or the object/system itself) [67%] 2023-12-19 [Systems]
18. Structure: Structure — дебютный проект российской студии Extent5 Game Studio и издательства «Бука» (Buka Entertainment). Релиз проекта ожидается во втором квартале 2018 года для PC. [67%] 2024-01-03
19. Structure (mathematical logic): In mathematical logic, the notion of a structure generalizes mathematical objects such as groups, rings, fields, lattices or ordered sets. A structure is a set equipped with any number of named constants, operations and relations. (Mathematical logic) [67%] 2023-08-04
20. Structure: A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as biological ... (Arrangement of interrelated elements in an object/system, or the object/system itself) [67%] 2024-01-03 [Structure]