Category:Definitions/Accumulation Points
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This category contains definitions related to Accumulation Points.
Related results can be found in Category:Accumulation Points.
Let $\struct {S, \tau}$ be a topological space.
Let $A \subseteq S$.
Accumulation Point of Sequence
Let $\sequence {x_n}_{n \mathop \in \N}$ be an infinite sequence in $A$.
Let $x \in S$.
Then $x \in S$ is an accumulation point of $\sequence {x_n}$ if and only if:
- $\forall U \in \tau: x \in U \implies \set {n \in \N: x_n \in U}$ is infinite
Accumulation Point of Set
Let $x \in S$.
Then $x$ is an accumulation point of $A$ if and only if:
- $x \in \map \cl {A \setminus \set x}$
where $\cl$ denotes the (topological) closure of a set.
Pages in category "Definitions/Accumulation Points"
The following 6 pages are in this category, out of 6 total.