A sequence ${x_i}_{i\in\mathbb N}$ in a topological space $X$ converges to $x \in X$ if for every open $U\subset X$ such that $x \in U$, there exists $n_0 \in\mathbb N$ such that for every $n \geq n_0$, we have $x_n \in U$.
In a general topological space, (i.e. in some non-Hausdorff spaces) the limit of a sequence need not be unique!