# Difference between revisions of "Heine-Borel Theorem"

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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 be a metric space

Let

Then

(1) is closed and bounded if and only if

(2) is compact

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