Measure, Integration & Real Analysis · Problem 2E.10

Integration — Sheldon Axler

Mathematics — Measure Theory · extension-of-continuous-functions-closed-sets

Problem

Suppose

F \subseteq \mathbf{R}

is such that every continuous function from

F

\mathbf{R}

can be extended to a continuous function from

\mathbf{R}

\mathbf{R}

. Prove that

F

is a closed subset of

\mathbf{R}