 Tietze extension theorem

In topology, the Tietze extension theorem states that, if X is a normal topological space and
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
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 R^{J} for some indexing set J, any retract of R^{J}, or any normal absolute retract whatsoever.
The theorem is due to Heinrich Franz Friedrich Tietze.
References
Categories: Mathematics stubs
 Continuous mappings
 Theorems in topology
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