Basic Analysis I — Real Analysis · Problem 3.2.13

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · continuous-functions

Problem

Let

f : S \to \mathbb{R}

be a function and

c \in S

, such that for every sequence

\{x_n\}_{n=1}^\infty

S

with

\lim_{n \to \infty} x_n = c

, the sequence

\bigl\{f(x_n)\bigr\}_{n=1}^\infty

converges. Show that

f

is continuous at

c