Hausdorff not implies collectionwise Hausdorff

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 need not satisfy the second topological space property
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Statement

A Hausdorff space need not be collectionwise Hausdorff.

Related facts

• Completely regular not implies collectionwise Hausdorff

Examples

• The Moore plane is an example of a completely regular space, which is not collectionwise Hausdorff. The bounding real line is an uncountable discrete set, but we cannot find a corresponding open cover.
• The Sorgenfrey plane is another example