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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. 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 ... [94%] 2023-12-21 [Categories in category theory] [General topology]...
6. 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) [87%] 2023-12-22
7. .properties: .properties (от англ. properties — свойства, параметры) — текстовый формат и одноимённое расширение имени файла. [87%] 2024-01-04
8. Properties: Properties are those entities that can be predicated of things or, in other words, attributed to them. Thus, properties are often called predicables. (Philosophy) [87%] 2022-05-04
9. .properties: .properties是一种主要在Java相关技术中用来存储应用程序的可配置参数的文件的文件扩展名。它们也可以存储用于国际化和本地化的字符串，这种文件被称为属性资源包（Property Resource Bundles）。 每个参数被存储为一对字符串：一个存储名称参数（被称为“键”），另一个存储值。 每个.properties 文件中的行通常存储单个属性。对于每一行可能有这么几种格式，包括键=值，键 = 值，键:值，以及键 值。 .properties文件可以使用井号（#）或叹号（!）作为一行中第一个非空白字符来表示它后面的所有文本都是一个注释。反斜杠（\）用于转义字符。下面提供一个属性文件的示例。 site是一个键，它对应的值是http://en.wikipedia.org/。而数字符号和感. [87%] 2025-04-05 [文件格式] [配置文件]...
10. 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 ... [84%] 2023-11-08 [General topology]
11. 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. [84%] 2024-10-05 [Categories in category theory] [General topology]...
12. 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]...
13. 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]...
14. 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
15. 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
16. 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]
17. 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]...
18. 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]...
19. 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]...
20. Propertius: Sextus Propertius was ’n Latynse treurdigter uit die Augustynse tydperk. Hy is tussen 50 en 45 v.C. [78%] 2024-01-03