Basic Analysis I — Real Analysis · Problem 3.1.6

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · limits-of-functions

Problem

Let

A \subset S

. Suppose

c

is a cluster point of

A

and it is also a cluster point of

S

. Let

f : S \to \mathbb{R}

be a function. Show that if

f(x) \to L

x \to c

, then

f|_A(x) \to L

x \to c

. Note the difference from Proposition 3.1.15.