Measure, Integration & Real Analysis · Problem 2E.11

Integration — Sheldon Axler

Mathematics — Measure Theory · extension-bounded-continuous-functions

Problem

Prove or give a counterexample: If

F \subseteq \mathbf{R}

is such that every bounded continuous function from

F

\mathbf{R}

can be extended to a continuous function from

\mathbf{R}

\mathbf{R}

, then

F

is a closed subset of

\mathbf{R}