# Definition:Weakly Hereditary Property

## Definition

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.