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.[1] A closed discrete set S of a topology X is one where every point of X has a neighborhood that intersects at most one point from S. Every T1 space which is collectionwise Hausdorff is also Hausdorff.
Metrizable spaces are collectionwise normal spaces and are hence, in particular, collectionwise Hausdorff.
References
- ↑ FD Tall, The density topology, Pacific Journal of Mathematics, 1976
This article is issued from Wikipedia - version of the Saturday, November 01, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.