Does a continuous map on a compact subset of $\mathbb{R}^n$ always have a compactly supported extension to $\mathbb{R}^n$?

Asked Jun 04 '21 at 16:13

Active Jun 04 '21 at 16:59

Viewed 37 times

Let $K$ be a compact subset of $\mathbb R^n$ and $f : K \to \mathbb R^p$ a continuous map. Is there always an extension $\tilde f$ of $f$ to $\mathbb R^n$ as a whole such that $\tilde f$ is continuous and compactly supported?

asked Jun 04 '21 at 16:13

KCJV

4

Wlog $p=1$, in which case this is precisely the Tietze Extension Theorem. – David C. Ullrich Jun 04 '21 at 16:27

Does a continuous map on a compact subset of $\mathbb{R}^n$ always have a compactly supported extension to $\mathbb{R}^n$?

0 Answers0