Word Pronunciation & Dictionary

hausdorff space

Word Rarity Very rare

Frequency: Zipf frequency 2.00 in modern English

Syllables: haus-dorf-f s-pace
IPA

28

Scrabble Score

14

Letters

4

Syllables

11

Unique Chars

Meaning

noun

A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that x∈U and y∈V.

Example Sentences

"More generally, each compact subset of a Hausdorff space is closed.[…]Metric spaces and compact Hausdorff spaces enjoy an even stronger separation property; in either case, disjoint closed sets can always be separated by disjoint open sets."
"In 1953, Grothendieck [G] characterized locally convex Hausdorff spaces which have the Dunford-Pettis property and used this property to characterize weakly compact operators u : C(K) → F, where K is a compact Hausdorff space and F is a locally compact Hausdorff space (briefly, lcHs) which is complete."
"Our construction of βD is a special case of more general constructions in which compact Hausdorff spaces are obtained using sets which are maximal subject to having certain algebraic properties."

Etymology

Named after German mathematician Felix Hausdorff (1868–1942).

Inflected Forms

Hausdorff spaces (plural)

Synonyms

T₂ space

Questions

What does hausdorff space mean?: A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that x∈U and y∈V.
Where does hausdorff space come from?: Named after German mathematician Felix Hausdorff (1868–1942).

How to pronounce hausdorff space

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