Basic Analysis I — Real Analysis · Problem 3.1.14

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · limits-of-functions

Problem

(Challenging) Show that the hypothesis that

g(c_2) = L

in Exercise 3.1.9 is necessary. That is, find

f

and

g

such that

f(x) \to c_2

x \to c_1

and

g(y) \to L

y \to c_2

, but

g\bigl(f(x)\bigr)

does not go to

L

x \to c_1