Lebl-Basic-Analysis-I · Problem 3.2.8

Continuous Functions

Mathematics · continuous-functions

Problem

Suppose

S \subset \mathbb{R}

, such that

(c - \alpha, c + \alpha) \subset S

for some

c \in \mathbb{R}

and

\alpha > 0

. Let

f : S \to \mathbb{R}

be a function and

A := (c - \alpha, c + \alpha)

. Prove that if

f|_A

is continuous at

c

, then

f

is continuous at

c