The usual proof presented for the Tietze Extension Theorem uses Urysohn's Lemma and some form
of the Weierstras M-Test--the extension of the given continuous function on a closed subset is
built using an infinite series of continuous functions whose convergence is assured by comparison
with a known (convergent) geometric series. An alternative approach is to build the extension
by means of the Katetov-Tong Insertion Lemma. We will present and prove this lemma and, if time
permits, apply it to prove the Tietze Extension Theorem.