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:
- $A \cap \paren {U \setminus \set x} \ne \O$
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 10 subcategories, out of 10 total.
A
- Accumulation Points (8 P)
C
- Condensation Points (10 P)
D
- Derived Sets (empty)
E
L
- Limit Points of Filter Bases (1 P)
O
- Omega-Accumulation Points (8 P)
Pages in category "Limit Points"
The following 21 pages are in this category, out of 21 total.
A
E
L
- Limit of Sequence is Accumulation Point
- 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 of Distinct Terms is Omega-Accumulation Point of Range
- Limit Point of Set may or may not be Element of Set
- Limit Point of Subset is Limit Point of Set
- Limit Point of Subset of Metric Space is at Zero Distance
- Local Basis Test for Limit Point