Urysohn is hereditary
This article gives the statement, and possibly proof, of a topological space property (i.e., Urysohn space) satisfying a topological space metaproperty (i.e., subspace-hereditary property of topological spaces)
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Statement
Any subset of a Urysohn space, endowed with the subspace topology, is also a Urysohn space.
Related facts
Similar facts
| Property | Proof that it is hereditary |
|---|---|
| Hausdorff space | Hausdorffness is hereditary |
| regular space | regularity is hereditary |
| completely regular space | complete regularity is hereditary |
| collectionwise Hausdorff space | [[collectionwise Hausdorff is hereditary] |
Other similar facts:
- Normality is weakly hereditary
- Compactness is weakly hereditary
- [[Monotone normality is hereditary]
Opposite facts
- [[Normality is not hereditary]