Continuity in terms of Preimage

Statements

Proposition. Let $(X,{\tau }_x)$ and $(Y,{\tau }_y)$ be topological spaces. A function $f:X\to Y$ is continuous if and only if, for every open set $V\subset Y$, the preimage of $V$ under $f$ is an open set of $X$.

References

@Tu11 Proposition A.23