# Category:Limit Points

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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:

- $A \cap \left({U \setminus \left\{{x}\right\}}\right) \ne \varnothing$

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 4 subcategories, out of 4 total.

### A

### C

### O

## Pages in category "Limit Points"

The following 30 pages are in this category, out of 30 total.

### L

- Limit Point iff Superfilter Converges
- Limit Point of Countable Open Set in Particular Point Space
- Limit Point of Sequence in Discrete Space not always Limit Point of Open Set
- Limit Point of Sequence is Accumulation Point
- Limit Point of Sequence is Adherent Point of Range
- Limit Point of Sequence may only be Adherent Point of Range
- Limit Point of Sequence of Distinct Terms is Omega-Accumulation Point of Range
- Limit Point of Subset is Limit Point of Set
- Limit Points in Closed Extension Space
- 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