topological space


: a set with a collection of subsets satisfying the conditions that both the empty set and the set itself belong to the collection, the union of any number of the subsets is also an element of the collection, and the intersection of any finite number of the subsets is an element of the collection

Examples of topological space in a Sentence

Recent Examples on the Web Mapping the Maps To classify shapes, or topological spaces, mathematicians distinguish between differences that matter and those that don’t. Kevin Hartnett, Quanta Magazine, 22 Aug. 2023 Homotopy is useful for classifying topological spaces — creating a chart of all the kinds of shapes that are possible. Kevin Hartnett, Quanta Magazine, 22 Aug. 2023 So a single topological space can be expressed as a category, but also, the totality of topological spaces can also be expressed as a category. Steven Strogatz, Quanta Magazine, 22 Mar. 2023 Their goal is to create new foundations for topology, replacing the traditional notion of a topological space — whose examples include the sphere and the doughnut — with more versatile objects that the authors call condensed sets. Quanta Magazine, 19 May 2015 Finally, there are the Sustainability Pragmatists (the Pragmatists), a rather small set in this topological space but with the promise to expand. Robert G. Eccles, Forbes, 3 June 2022 Calling out activist investors, seen by many as the most rapacious of capitalists and not a bunch of ESG sissies, nicely illustrates just how complicated this topological space is. Robert G. Eccles, Forbes, 3 June 2022 See More

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'topological space.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

First Known Use

1926, in the meaning defined above

Time Traveler
The first known use of topological space was in 1926

Dictionary Entries Near topological space

Cite this Entry

“Topological space.” Dictionary, Merriam-Webster, Accessed 9 Dec. 2023.

More from Merriam-Webster on topological space

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!