collectionwise Hausdorff

5 examples (0.02 sec)
  • A collectionwise normal T 1 space is a collectionwise Hausdorff space.
  • Metrizable spaces are collectionwise normal spaces and are hence, in particular, collectionwise Hausdorff.
  • An extremally disconnected first countable collectionwise Hausdorff space must be discrete.
  • 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.
  • 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.