Topological space - Wikipedia
A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. [1] [2] Common types of topological spaces include Euclidean spaces, metric spaces and manifolds.
拓扑空间 - 维基百科，自由的百科全书
拓扑空间（英語： Topological space ）是一种賦予「一點附近」這個概念的抽象数学结构；拓扑空间也是一个集合，其元素称为点，由此可以定義出如收敛、连通、连续等概念。
Topology - Wikipedia
A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of topological spaces, as any distance or metric defines a topology.
Topological Space -- from Wolfram MathWorld
6 days ago · A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set emptyset is in T. 2. X is in T. 3. The intersection of a finite number of sets in T is also in T. 4.
Topology -- from Wolfram MathWorld
3 days ago · A set for which a topology has been specified is called a topological space (Munkres 2000, p. 76). For example, the set together with the subsets comprises a topology, and is a topological space. Topologies can be built up from topological bases. For the real numbers, a topological basis is the set of open intervals.
Topology/Topological Spaces - Wikibooks, open books for an …
Nov 6, 2017 · The ordered pair (,) is called a topological space. This definition of a topological space allows us to redefine open sets as well. Previously, we defined a set to be open if it contained all of its interior points, and the interior of a set was defined by open balls, which required a metric .
Topological space | Compactness, Connectedness & Separation
Topological space, in mathematics, generalization of Euclidean spaces in which the idea of closeness, or limits, is described in terms of relationships between sets rather than in terms of distance. Every topological space consists of: (1) a set of points; (2) a class of subsets defined
A set X with a topology T is called a topological space. An element of T is called an open set. Example 1.2. Example 1, 2, 3 on page 76,77 of [Mun] Example 1.3. Let X be a set. (Finite complement topology) Define T to be the collection of all subsets U of X such that X U either is finite or is all of X.
What is Topology? | Pure Mathematics - University of Waterloo
Topology studies properties of spaces that are invariant under any continuous deformation. It is sometimes called "rubber-sheet geometry" because the objects can be stretched and contracted like rubber, but cannot be broken. For example, a square can be deformed into a circle without breaking it, but a figure 8 cannot.
Topology | Brilliant Math & Science Wiki
Topology is the study of properties of geometric spaces which are preserved by continuous deformations (intuitively, stretching, rotating, or bending are continuous deformations; tearing or gluing are not).