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.