Tietze extension theorem

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The Tietze extension theorem in topology states that, if X is a normal topological space and

f : AR

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 : XR

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.

de:Fortsetzungssatz von Tietze