# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 77: Mapping Continuity (Topology)

In topology, a mapping $f: X \rightarrow Y$ between topological spaces $X, Y$ is continuous if the pre-image of every open subset of $Y$ is itself an open subset of $X$.

(An equivalent condition/definition is that the pre-image of every closed subset of $Y$ is itself a closed subset of $X$.)