TITLE: Applications of Tietze Extension Theorem
QUESTION [13 upvotes]: I'm searching for some nice applications of Tietze extension theorem, in any area of mathematics. Can you name some (and possibly give references) to me?
Thank you in advance!

REPLY [2 votes]: I'm not sure if the following proof works, but it uses the Tietze extension theorem, among other things, to prove the density of $C_{0}(\mathbb{R})$ in $L^{1}$.