Continuous Map Between Topological Spaces

Let $(X,\mathcal{T}_X)$ and $(Y,\mathcal{T}_Y)$ be topological spaces, and let $f:X\to Y$ be a function. We say that $f$ is continuous if for every open set $V\in\mathcal{T}_Y$, the inverse image

$$f^{-1}(V)=\{x\in X : f(x)\in V\}$$

belongs to $\mathcal{T}_X$.