topological space

noun

, Mathematics.

1. 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

1. 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

Word History and Origins

Origin of topological space¹

First recorded in 1945–50

Example Sentences

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.

From Scientific American

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.

From Scientific American

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

From Washington Post

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

From The Guardian