Subspace operator

Definition
The subspace operator is a property modifier that takes as input a property $$p$$ of topological spaces, and outputs the property of being a topological space which embeds as a subspace of some topological space with property $$p$$. Note that $$p$$ is a fixed-point of the subspace operator iff $$p$$ is itself subspace-hereditary.

A related, but opposite, operator is the hereditarily operator.