Collectionwise Hausdorffness is hereditary
This article gives the statement, and possibly proof, of a topological space property (i.e., collectionwise Hausdorff space) satisfying a topological space metaproperty (i.e., subspace-hereditary property of topological spaces)
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Statement
Any subset of a collectionwise Hausdorff space, endowed with the subspace topology, is also a collectionwise Hausdorff space.
Related facts
Similar facts
| Property | Proof that is is subspace-hereditary |
|---|---|
| Hausdorff space | Hausdorffness is hereditary |
| regular space | regularity is hereditary |
| Urysohn space | Urysohn is hereditary |
| T1 space | T1 is hereditary |
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