In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary.
== Formal statement ==
If X is a normal topological space and
f
:
A
→
R
{\displaystyle f:A\to \mathbb {R} }
is a continuous map from a closed subset A of X into the real numbers carrying the standard topology, then there exists a continuous map...
