Tietze extension theorem
From Wikipedia, the free encyclopedia
In topology, the Tietze extension theorem 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.
The theorem is due to Heinrich Franz Friedrich Tietze.
