# Category:Examples of Limit Points

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This category contains examples of **Limit Point** in the context of **Topology**.

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 $x$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Examples of Limit Points"

The following 20 pages are in this category, out of 20 total.

### L

- Limit Point/Examples
- Limit Point/Examples/End Points of Real Interval
- Limit Point/Examples/Union of Singleton with Open Real Interval
- Limit Points in Excluded Point Space
- Limit Points in Fort Space
- Limit Points in Open Extension Space
- Limit Points in Particular Point Space
- Limit Points in T1 Space
- Limit Points in Uncountable Fort Space
- Limit Points of Countable Complement Space
- Limit Points of Either-Or Topology
- Limit Points of Indiscrete Space
- Limit Points of Infinite Subset of Finite Complement Space
- Limit Points of Open Real Interval