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Cantor Intersection Theorem (view source)
Revision as of 19:48, February 17, 2008
, 19:48, February 17, 2008link to mathematician
If '''<math>F_n</math>''' is a collection of closed subspaces of a [[complete metric space]] such that <math>F_{n+1} \in F_n</math> for all '''<math>n</math>''' and <math>\lim_{n \to \infty} diameter(F_n) = 0</math>, then '''∩ <math>F_n</math>''' is a single point.
If '''<math>F_n</math>''' is a collection of closed subspaces of a [[complete metric space]] such that <math>F_{n+1} \in F_n</math> for all '''<math>n</math>''' and <math>\lim_{n \to \infty} diameter(F_n) = 0</math>, then '''∩ <math>F_n</math>''' is a single point.
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This [[theorem]] was proven by [[Georg Cantor]].
[[category: mathematics]]
[[category: mathematics]]