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