Difference between revisions of "Tietze Extension Theorem"
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If ''A'' is a closed subspace in a [[normal space]] ''X'' and ''f : A → [p, q]'' is a [[continuous function]], then there exists a continuous function ''F : X → [p, q]'' such that ''F|<sub>A</sub> = f''. | If ''A'' is a closed subspace in a [[normal space]] ''X'' and ''f : A → [p, q]'' is a [[continuous function]], then there exists a continuous function ''F : X → [p, q]'' such that ''F|<sub>A</sub> = f''. | ||
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Latest revision as of 20:34, July 13, 2016
The Tietze Extension Theorem states:
If A is a closed subspace in a normal space X and f : A → [p, q] is a continuous function, then there exists a continuous function F : X → [p, q] such that F|A = f.