Category:Open subspace-closed properties of topological spaces

This category lists properties of topological spaces that are inherited by all open subsets. In other words, if ${\displaystyle X}$ is a topological space satisfying the given property, and ${\displaystyle U}$ is an open subset of ${\displaystyle X}$, then ${\displaystyle U}$, endowed with the subspace topology, also satisfies the given property.

Note that those properties which are inherited by all subsets are not listed here, but can be found at:

Category:Subspace-hereditary properties of topological spaces

Properties inherited by closed subsets can be found at:

Category:Weakly hereditary properties of topological spaces