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The '''Cantor Intersection Theorem''' states:  
 
The '''Cantor Intersection Theorem''' states:  
 
<blockquote>
 
<blockquote>
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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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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>
 
</blockquote>
 
[[category: mathematics]]
 
[[category: mathematics]]
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