# Category:Uniformly Continuous Mappings

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This category contains results about **uniformly continuous mappings** in the context of **metric spaces**.

Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.

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

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

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

## Subcategories

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

### H

- Heine-Cantor Theorem (3 P)

### U

## Pages in category "Uniformly Continuous Mappings"

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