Category:Limit Points

This category contains results about Limit Points in the context of Topology.
Definitions specific to this category can be found in Definitions/Limit Points.

A point $x \in S$ is a limit point of $A$ if and only if every open neighborhood $U$ of $x$ satisfies:

$A \cap \paren {U \setminus \set x} \ne \O$

That is, if and only if every open set $U \in \tau$ such that $x \in U$ contains some point of $A$ distinct from $x$.

More symbolically, a point $x \in S$ is a limit point of $A$ if and only if

$\forall U\in \tau :x\in U \implies A \cap \paren {U \setminus \set x} \ne \O\text{.}$