Tietze extension theorem
with F(a) = f(a) for all a in A. Moreover, F may be chosen such that , i.e., if f is bounded, F may be chosen to be bounded (with the same bound as f). 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.
- Hazewinkel, Michiel, ed. (2001), "Urysohn-Brouwer lemma", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Weisstein, Eric W. "Tietze's Extension Theorem." From MathWorld
- Tietze extension theorem, PlanetMath.org.
- Proof of Tietze extension theorem, PlanetMath.org.
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