Hausdorff space

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(topology) 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.

日本語の意味

ハウスドルフ空間：任意の2つの異なる点について、それぞれを含みながら互いに交わらない開集合が存在する位相空間（トポロジカルスペース）のこと。

英語の意味

(topology) 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.

このボタンはなに？

In a Hausdorff space, every convergent sequence has a unique limit.

ハウスドルフ空間では、収束する列は一意の極限を持つ。

詳細

意味（1）

(topology) 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.

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.

詳細

Hausdorff spaces （ plural ）