Definition:Continuous Mapping (Topology)/Everywhere

Definition
Let $T_1 = \left({S_1, \tau_1}\right)$ and $T_2 = \left({S_2, \tau_2}\right)$ be topological spaces.

Let $f: S_1 \to S_2$ be a mapping from $S_1$ to $S_2$.

Also known as
If it is necessary to distinguish between multiple topologies on the same set, then the terminology $\left({\tau_1, \tau_2}\right)$-continuous can be used for the above.

Also see

 * Equivalence of Definitions of Everywhere Continuous Mapping between Topological Spaces