# Definition:Hereditary Property (Topology)

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## Definition

Let $\xi$ be a property whose domain is the set of all topological spaces.

Then $\xi$ is a hereditary property if and only if:

$\map \xi X \implies \map \xi Y$

where $Y$ is a subspace of $X$.

That is, whenever a topological space has $\xi$, then so does any subspace.