Limit point

This article is about a basic definition in topology.
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Definition

Let $X$ be a topological space, $A$ a subset of $X$, and $x\in X$ a point ($x$ may or may not belong to $A$). We say that $x$ is a limit point of $A$ if given any open subset $U\ni x$ in $X$, $(U\setminus x)\cap A$ is nonempty.

Relation with other properties

• Cluster point
• Accumulation point
• Isolated point