- Tietze extension theorem
In topology, the Tietze extension theorem states that, if X is a normal topological space and
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. It can be generalized by replacing R with RJ for some indexing set J, any retract of RJ, or any normal absolute retract whatsoever.
The theorem is due to Heinrich Franz Friedrich Tietze.
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