#
Homotopy Type Theory
uniformly continuous function > history (Rev #3)

# Contents

Whenever editing is allowed on the nLab again, this article should be ported over there.

## Definition

#### In Archimedean ordered fields

Let $F$ be an Archimedean ordered field and let

$F_{+} \coloneqq \sum_{a:F} 0 \lt a$

be the positive elements in $F$. A function $f:F \to F$ is **uniformly continuous** in $F$ if

$isUniformlyContinuous(f) \coloneqq \prod_{\epsilon:F_{+}} \Vert \sum_{\delta:F_{+}} \prod_{x:F} \prod_{y:F} (\vert x - y \vert \lt \delta) \to (\vert f(x) - f(y) \vert \lt \epsilon) \Vert$

## See also

Revision on June 10, 2022 at 01:28:44 by
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