# Category:Uniformly Continuous Mappings

Jump to navigation
Jump to search

This category contains results about Uniformly Continuous Mappings in the context of Metric Spaces.

Let $M_1 = \left({A_1, d_1}\right)$ and $M_2 = \left({A_2, d_2}\right)$ be metric spaces.

Then a mapping $f: A_1 \to A_2$ is **uniformly continuous on $A_1$** if and only if:

- $\forall \epsilon \in \R_{>0}: \exists \delta \in \R_{>0}: \forall x, y \in A_1: d_1 \left({x, y}\right) < \delta \implies d_2 \left({f \left({x}\right), f \left({y}\right)}\right) < \epsilon$

where $\R_{>0}$ denotes the set of all strictly positive real numbers.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Uniformly Continuous Mappings"

The following 7 pages are in this category, out of 7 total.