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