Difference between revisions of "Heine-Borel Theorem"

m (Statement)
(Statement)
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==Statement==
 
==Statement==
Let <math>X</math> be a [[Metric|metric space]]
+
Let <math>X</math> be a [[Metric space]]
  
 
Let <math>E\subset X</math>
 
Let <math>E\subset X</math>

Revision as of 03:28, 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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