# Category:Convergent Sequences (Metric Space)

This category contains results about Convergent Sequences (Metric Space).
Definitions specific to this category can be found in Definitions/Convergent Sequences (Metric Space).

Let $M = \left({A, d}\right)$ 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:

$\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: \forall n \in \N: n > N \implies \map d {x_n, l} < \epsilon$

## Subcategories

This category has only the following subcategory.

## Pages in category "Convergent Sequences (Metric Space)"

This category contains only the following page.