Difference between revisions of "Tietze Extension Theorem"

Theorem

Let $(X,\tau)$ be a normal topological space, let $A \subset X$ be closed, and let $f \colon A \rightarrow \mathbb{R}$ be a continuous function (where $\mathbb{R}$ is equipped with the Euclidean topology). Then there exists a continuous function $F \colon X \rightarrow \mathbb{R}$ such that for all $a \in A$, $F(a)=f(a)$.