# Difference between revisions of "Heine-Borel Theorem"

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− | The '''Heine-Borel theorem''' is an important theorem in elementary [[ | + | The '''Heine-Borel theorem''' is an important theorem in elementary [[topology]]. |

==Statement== | ==Statement== | ||

− | Let <math>X</math> be | + | Let <math>X</math> be any [[metric space]] and <math>E \subseteq X</math> any [[subset]]. Then <math>E</math> is [[compact set | compact]] if and only if <math>E</math> is [[closed]] and [[bounded]]. |

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{{stub}} | {{stub}} | ||

[[Category:Topology]] | [[Category:Topology]] |

## Revision as of 17:27, 15 February 2008

The **Heine-Borel theorem** is an important theorem in elementary topology.

## Statement

Let be any metric space and any subset. Then is compact if and only if is closed and bounded.

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