Category:Coarsening-preserved properties of topological spaces

This category lists coarsening-preserved properties of topological spaces. This means that if ${\displaystyle X}$ has topologies ${\displaystyle \tau ,{\tau }^{\prime }}$ and ${\displaystyle {\tau }^{\prime }}$ is a coarser topology than ${\displaystyle \tau }$, then:

${\displaystyle (X,\tau )}$ has the property implies that ${\displaystyle (X,{\tau }^{\prime })}$ has the property