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Tietze extension theorem

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.

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Tietze extension theorem".