Collectionwise Hausdorff space

In mathematics, in the field of topology, a topological space is said to be collectionwise Hausdorff if given any closed discrete collection of points in the topological space, there are pairwise disjoint open sets containing the points. Every T1 space which is collectionwise Hausdorff is also Hausdorff.

Metrizable spaces are collectionwise normal spaces and are hence, in particular, collectionwise Hausdorff.

This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Topology Properties of topological spaces Topology stubs Wikimedia Foundation. 2010. Игры ⚽ Нужен реферат? Koos Kombuis Ahmad Muhamman Yaqub Look at other dictionaries: Collectionwise normal space — In mathematics, a topological space X is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of X there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊂ Ui. A family of subsets of… …   Wikipedia Collectionwise normal — In mathematics, a topological space X is called collectionwise normal if for every discrete family F i ( i isin; I ) of closed subsets of X there exists a pairwise disjoint family of open sets U i ( i isin; I ), such that F i sub; U i . A family… …   Wikipedia Extremally disconnected space — In mathematics, a topological space is termed extremally disconnected or extremely disconnected if the closure of every open set in it is open. (The term extremally disconnected is usual, even though the word extremally does not appear in most… …   Wikipedia Moore space (topology) — In mathematics, more specifically point set topology, a Moore space is a developable regular Hausdorff space. Equivalently, a topological space X is a Moore space if the following conditions hold: Any two distinct points can be separated by… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”