English Dictionary

regular space

名詞

(topology) A Hausdorff space with the additional property that for every closed set of that space and every point disjoint from that set, there are a disjoint pair of open sets which contain the closed set and the point, respectively.

日本語の意味

正則空間：位相空間の一種で、ハウスドルフ性（T2性）を満たし、任意の閉集合とその閉集合に属さない点について、それぞれを含む交わらない開集合が存在する空間。

In many proofs in point-set topology, constructing a continuous function that separates a closed set and a point often relies on the space being a regular space.

点集合位相の多くの証明では、閉集合とその外の点を分離する連続写像を構成するために、空間が正規空間であることに依存することが多い。

意味（1）

(topology) A Hausdorff space with the additional property that for every closed set of that space and every point disjoint from that set, there are a disjoint pair of open sets which contain the closed set and the point, respectively.

regular spaces （ plural ）