collectionwise normal

5 examples (0.02 sec)
  • Every metrizable space (i. e., every topological space that is homeomorphic to a metric space) is collectionwise normal.
  • The Moore metrisation theorem states that every collectionwise normal Moore space is metrizable.
  • A collectionwise normal T 1 space is a collectionwise Hausdorff space.
  • It is a common tool to prove other metrization theorems, e.g. the Moore metrization theorem: a collectionwise normal, Moore space is metrizable, is a direct consequence.
  • Every collectionwise normal space is normal (i. e., any two disjoint closed sets can be separated by neighbourhoods), and every paracompact space (i. e., every topological space in which every open cover admits a locally finite open refinement) is collectionwise normal.