topological space
noun
: 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
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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
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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
Cite this Entry
“Topological space.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/topological%20space. Accessed 3 Jul. 2025.
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