In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. That is, a topological space X is a Moore space if the following conditions hold:
* Any two distinct points can be separated by neighbourhoods, and any closed set and any point in its complement can be separated by neighbourhoods. (X is a regular Hausdorff space.)
* There is a countable collection of open covers of X, such that for any closed set C and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from C. (X is a developable space.)
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| - Espace de Moore (topologie) (fr)
- 무어 공간 (ko)
- Moore space (topology) (en)
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| - ( 다른 뜻에 대해서는 무어 공간 (대수적 위상수학) 문서를 참고하십시오.) 일반위상수학에서 무어 공간(Moore空間, 영어: Moore space)은 거리화 가능 공간과 유사한 성질을 갖는 위상 공간이다. 일부 추가 조건 아래, 무어 공간과 거리화 가능 공간의 조건은 서로 동치이다. (ko)
- In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. That is, a topological space X is a Moore space if the following conditions hold:
* Any two distinct points can be separated by neighbourhoods, and any closed set and any point in its complement can be separated by neighbourhoods. (X is a regular Hausdorff space.)
* There is a countable collection of open covers of X, such that for any closed set C and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from C. (X is a developable space.) (en)
- En mathématiques, plus spécifiquement en topologie, un espace de Moore est un espace séparé, régulier et développable. Plus précisément, un espace topologique X est un espace de Moore si les conditions suivantes sont réunies : Le concept d'espace de Moore a été formulé par Robert Lee Moore dans la première partie du XXe siècle. Les questions se posant sur les espaces de Moore concernent généralement leur métrisabilité : quelles conditions naturelles faut-il ajouter à un espace de Moore pour s'assurer qu'il soit métrisable ? (fr)
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| - In mathematics, more specifically point-set topology, a Moore space is a developable regular Hausdorff space. That is, a topological space X is a Moore space if the following conditions hold:
* Any two distinct points can be separated by neighbourhoods, and any closed set and any point in its complement can be separated by neighbourhoods. (X is a regular Hausdorff space.)
* There is a countable collection of open covers of X, such that for any closed set C and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from C. (X is a developable space.) Moore spaces are generally interesting in mathematics because they may be applied to prove interesting metrization theorems. The concept of a Moore space was formulated by R. L. Moore in the earlier part of the 20th century. (en)
- En mathématiques, plus spécifiquement en topologie, un espace de Moore est un espace séparé, régulier et développable. Plus précisément, un espace topologique X est un espace de Moore si les conditions suivantes sont réunies :
* X est séparé : deux points distincts admettent des voisinages disjoints ;
* X est régulier : tout ensemble fermé et tout point de son complémentaire admettent des voisinages disjoints ;
* X est développable : il existe une famille dénombrable de recouvrements ouverts de X, de telle sorte que pour tout ensemble fermé C et tout point p de son complémentaire, il existe un recouvrement dans telle que chaque voisinage de p dans est disjoint de C. Une telle famille est appelée un développement de X. Le concept d'espace de Moore a été formulé par Robert Lee Moore dans la première partie du XXe siècle. Les questions se posant sur les espaces de Moore concernent généralement leur métrisabilité : quelles conditions naturelles faut-il ajouter à un espace de Moore pour s'assurer qu'il soit métrisable ? (fr)
- ( 다른 뜻에 대해서는 무어 공간 (대수적 위상수학) 문서를 참고하십시오.) 일반위상수학에서 무어 공간(Moore空間, 영어: Moore space)은 거리화 가능 공간과 유사한 성질을 갖는 위상 공간이다. 일부 추가 조건 아래, 무어 공간과 거리화 가능 공간의 조건은 서로 동치이다. (ko)
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