Convergence by topology

Let $(X, \tau)$ - a topological-space.

Sequence ${x_n}_1^{\infty} \subset X$ converges to $x \in X$ if $$ \forall U(x) \in \tau: (\exists N \in \mathbb{N})(\forall n \geq N) \hookrightarrow x_n \in U(x) $$

Here $U(x)$ is an $x$ point-neighborhood