Closure of a Subset of a Topological Space

Let $(X,\mathcal{T})$ be a topological space, and let $A\subseteq X$. The closure of $A$ in $X$ is the subset

$$\operatorname{cl}_X(A)=\{x\in X:\ U\cap A\neq\varnothing \text{ for every } U\in\mathcal{T} \text{ with } x\in U\}$$

of $X$. Its elements are called the adherent points of $A$ in $X$. When the ambient space $X$ is clear from context, the closure of $A$ in $X$ is also written $\overline{A}$.