Category:Definitions/Convergent Sequences (Topology)
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This category contains definitions related to convergent sequences in the context of topology.
Related results can be found in Category:Convergent Sequences (Topology).
Let $T = \struct {S, \tau}$ be a topological space.
Let $A \subseteq S$.
Let $\sequence {x_n}_{n \mathop \in \N}$ be an infinite sequence in $A$.
Then $\sequence {x_n}$ converges to the limit $\alpha \in S$ if and only if:
- $\forall U \in \tau: \alpha \in U \implies \paren {\exists N \in \R_{>0}: \forall n \in \N: n > N \implies x_n \in U}$
Pages in category "Definitions/Convergent Sequences (Topology)"
The following 6 pages are in this category, out of 6 total.
C
- Definition:Convergent Sequence in Strong Operator Topology
- Definition:Convergent Sequence in Uniform Operator Topology
- Definition:Convergent Sequence in Weak Operator Topology
- Definition:Convergent Sequence/Topology
- Definition:Convergent Sequence/Topology/Definition 1
- Definition:Convergent Sequence/Topology/Definition 2