ThmDex – An index of mathematical definitions, results, and conjectures.

Proof P3355 on R1276: Every map from discrete topological space is continuous

P3355

For all open sets $U \in \mathcal{T}_Y$ in $T_Y$, we have $f^{-1} U \subseteq X$ by definition of a preimage and thus $f^{-1} U \in \mathcal{P}(X)$. The claim therefore is a consequence of result R324: Continuity characterised by preimages of open sets. $\square$