Hausdorff not implies collectionwise Hausdorff

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