Basic Analysis I — Real Analysis · Problem 6.1.3

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · uniform-convergence-restrictions

Problem

Suppose

f_n : S \to \mathbb{R}

are functions that converge uniformly to

f : S \to \mathbb{R}

. Suppose

A \subset S

. Show that the sequence of restrictions

\{f_n|_A\}_{n=1}^\infty

converges uniformly to

f|_A