# Limit point

A metric space $E$ is called complete if every fundamental sequence in $E$ converges to some element of the space. If each neighborhood of a point $f \subset E$ contains infinitely many points of a set $M$ in $E$, then $f$ is called a limit point of $M$. If a set contains all its limit points then it is said to be closed. The set consisting of $M$ and its limit points is called the closure of $M$ and is denoted by $\bar{M}$.[1]
If $A$ is a subset of the topological space $X$ and if $x$ is a point of $X$, then $x$ is a limit point of $A$ if every neighborhood of $x$ intersects $A$ in some point other than itself.[2]