Category:Definitions/Convergent Sequences (Metric Space)
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This category contains definitions related to convergent sequences in the context of metric spaces.
Related results can be found in Category:Convergent Sequences (Metric Space).
Let $M = \struct {A, d}$ be a metric space or a pseudometric space.
Let $\sequence {x_k}$ be a sequence in $A$.
$\sequence {x_k}$ converges to the limit $l \in A$ if and only if:
- $\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: \forall n \in \N: n > N \implies \map d {x_n, l} < \epsilon$
Pages in category "Definitions/Convergent Sequences (Metric Space)"
The following 7 pages are in this category, out of 7 total.
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- Definition:Convergent Sequence (Metric Space)
- Definition:Convergent Sequence in Metric Space
- Definition:Convergent Sequence/Metric Space
- Definition:Convergent Sequence/Metric Space/Definition 1
- Definition:Convergent Sequence/Metric Space/Definition 2
- Definition:Convergent Sequence/Metric Space/Definition 3
- Definition:Convergent Sequence/Metric Space/Definition 4