Lebl-Basic-Analysis-I · Problem 3.4.11

Continuous Functions

Mathematics · uniform-continuity

Problem

Prove: a) If

f : S \to \mathbb{R}

and

g : S \to \mathbb{R}

are uniformly continuous, then

h : S \to \mathbb{R}

given by

h(x) := f(x) + g(x)

is uniformly continuous. b) If

f : S \to \mathbb{R}

is uniformly continuous and

a \in \mathbb{R}

, then

h : S \to \mathbb{R}

given by

h(x) := af(x)

is uniformly continuous.