Limit point

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