Difference between revisions of "Tietze Extension Theorem"
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(New page: The '''Tietze Extension Theorem''' states: <blockquote> If ''A'' is a closed subspace in a normal ''X'' and ''f : A → [p, q]'' is a continuous function, then there exists a continuou...) |
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The '''Tietze Extension Theorem''' states: | The '''Tietze Extension Theorem''' states: | ||
<blockquote> | <blockquote> | ||
| − | If ''A'' is a closed subspace in a normal ''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''. |
</blockquote> | </blockquote> | ||
[[category:topology]] | [[category:topology]] | ||
Revision as of 02:38, April 7, 2007
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.
