Definition:Weakly Hereditary Property

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

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

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

where $Y$ is any closed set of $X$ when considered as a subspace.

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

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