Topological Closures

Definition

Given a set $A$ of a topological space, a point $x$ is said to be in the closure of $A$ if, for each neighborhood $N$ of $X$, $N \cap A \neq \varnothing$. The closure of $A$ is the set of such points.

Notation

The closure of a set $A$ of a topological space is denoted $\bar{A}$. Other notation includes $\cl(A)$.