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Cantor Intersection Theorem (view source)
Revision as of 18:01, April 6, 2007
, 18:01, April 6, 2007New page: The '''Cantor Intersection Theorem''' states: <blockquote> 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</ma...
The '''Cantor Intersection Theorem''' states:
<blockquote>
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.
</blockquote>
[[category: mathematics]]
<blockquote>
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.
</blockquote>
[[category: mathematics]]