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topological space
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A topological space is a mathematical structure consisting of a set of points along with a defined collection of neighborhoods around those points that follow specific rules. This framework matters because it provides a general way to study properties like continuity and connectedness that don't depend on measuring distances, making it useful across many areas of mathematics.
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Wikidata facts
- Subclass of
- mathematical structure
- Named after
- space
- Image
- Topological space examples.svg
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- Commons category
- Topology
- topic's main category
- Category:Topological spaces
- studied by
- general topology
- has characteristic
- category of topological spaces
- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- maintained by WikiProject
- WikiProject Mathematics
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Encyclopedic overview
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 an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets.
A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Common types of topological spaces include Euclidean spaces, metric spaces and manifolds.
Excerpted from Wikipedia’s “topological space” article, available under the CC BY-SA 4.0 licence.