# Completely regular not implies collectionwise Hausdorff

From Topospaces

This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Completely regular space (?)) neednotsatisfy the second topological space property (i.e., Collectionwise Hausdorff space (?))

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## Statement

A completely regular space need not be a collectionwise Hausdorff space.

## Proof

### Examples

- The Moore plane is an example: See Moore plane is completely regular and Moore plane is not collectionwise Hausdorff
- The Sorgenfrey plane is another example: See Sorgenfrey plane is completely regular and Sorgenfrey plane is not collectionwise Hausdorff