Tietze extension theorem
From Wikipedia, the free encyclopedia
The Tietze extension theorem in topology states that, if X is a normal topological space and
-
- f : A → 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
-
- F : X → R
with F(a) = f(a) for all a in A. F is called a continuous extension of f.
The theorem generalizes Urysohn's lemma and is widely applicable, since all metric spaces and all compact Hausdorff spaces are normal.
