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Definition: Uniformly Continuous Functions (General Metric Spaces Case)
Let $(X,d_X)$ and $(Y,d_Y)$ be metric spaces. A function $f:X\mapsto Y$ is called uniformly continuous, if and only if for every $\epsilon > 0$ there is a $\delta > 0$ such that
$$d_Y(f(x),f(y)) < \epsilon$$
for all $x,y\in X$ with $$d_X(x,y) < \delta.$$
Table of Contents
- Theorem: Continuous Functions on Compact Domains are Uniformly Continuous
Mentioned in:
Proofs: 1
Theorems: 2
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References
Bibliography
- Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984
