Completely Hausdorff Space

A completely Hausdorff space, or functionally Hausdorff space, is a space in which any two distinct points can be separated by a function.

Read more about Completely Hausdorff SpaceNaming Conventions, Relation To Other Separation Axioms, Examples

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Completely Hausdorff Space - Examples
... This space is completely Hausdorff and Urysohn, but not regular (and thus not Tychonoff) ... There are obscure examples of spaces which are Hausdorff but not Urysohn, and spaces which are Urysohn but not completely Hausdorff or regular Hausdorff ...

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