Difference between revisions of "Heine-Borel Theorem"

(New page: The '''Heine-Borel theorem''' is an important theorem in elementary Topology. ==Statement== Let <math>X</math> be a metric space Let <math>E\subset X</math> Then (1) <m...)
 
m (Statement)
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(1) <math>E</math> is closed and bounded if and only if
 
(1) <math>E</math> is closed and bounded if and only if
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(2) <math>E</math> is [[Compact set|compact]]
 
(2) <math>E</math> is [[Compact set|compact]]
  

Revision as of 03:25, 15 February 2008

The Heine-Borel theorem is an important theorem in elementary Topology.

Statement

Let $X$ be a metric space

Let $E\subset X$

Then

(1) $E$ is closed and bounded if and only if

(2) $E$ is compact

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