Definition:Hereditary Property (Topology)

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

Then $\xi$ is hereditary iff:
 * $\xi \left({X}\right) \implies \xi \left({Y}\right)$

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

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

Also see

 * Weakly hereditary property