Limit point

• categories: Real Analysis, Definition

Definition

$p\in X$ is a limit point of $E$ if every neighborhood of $p$ contains a point $q\in E$

• Isolated point: if $p\in X$ is the only point in the neighborhood
• Inner point: if some neighborhood is fully contained in $E$

Theorem

If $p$ is a limit point of $E$ then every neighborhood contains infinitely many points in $E$