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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.
09-23-2007 01:00:40
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details