TOPOLOGICAL SPACE Definition & Meaning

topological space

noun

Mathematics.

a set with a collection of subsets or open sets satisfying the properties that the union of open sets is an open set, the intersection of two open sets is an open set, and the given set and the empty set are open sets.

topological space

noun

maths a set S with an associated family of subsets τ that is closed under set union and finite intersection. S and the empty set are members of τ

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51�Թ� History and Origins

Origin of topological space¹

First recorded in 1945–50

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Example Sentences

Examples have not been reviewed.

So we can characterize a topological space X by probing it with continuous functions f: T → X mapping out other spaces T. For instance, the points of the space X correspond to continuous functions x: * → X, whose domain is a space with a single point.

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We can use the points and paths of a space to translate problems of topology into problems of algebra: each topological space X has an associated category π1X called the “fundamental groupoid” of X. The objects of this category are the points of the space, and the transformations are paths.

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“Dante has invented a new topological space, the 3-sphere,” or hypersphere, mathematician Mark Peterson noted in an analysis.

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Britannica defines the Klein bottle thus:Topological space, named for the German mathematician Felix Klein.

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