collectionwise normal
A Hausdorff topological space X is called collectionwise normal if any discrete collection of sets {Ui} in X can be covered by a pairwise-disjoint collection of open sets {Vj} such that each Vj covers just one Ui. This is equivalent
to requiring the same property for any discrete collection of closed sets
.
A Hausdorff topological space X is called countably collectionwise normal if any countable discrete collection of sets {Ui} in X can be covered by a pairwise-disjoint collection of open sets {Vj} such that each Vj covers just one Ui. This is equivalent to requiring the same property for any countable discrete collection of closed sets.
Any metrizable space is collectionwise normal.
References
- 1 Steen, Lynn Arthur and Seebach, J. Arthur, Counterexamples in Topology, Dover Books, 1995.
Title | collectionwise normal |
---|---|
Canonical name | CollectionwiseNormal |
Date of creation | 2013-03-22 14:49:54 |
Last modified on | 2013-03-22 14:49:54 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 5 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 54D20 |
Defines | countably collectionwise normal |