# Category:Limit Points

Jump to navigation
Jump to search

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 $x$.

## Subcategories

This category has the following 8 subcategories, out of 8 total.

### A

### C

### L

### O

## Pages in category "Limit Points"

The following 34 pages are in this category, out of 34 total.

### A

### L

- Limit Point iff Superfilter Converges
- Limit Point in Metric Space iff Limit Point in Topological 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 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
- Local Basis Test for Limit Point