Difference between revisions of "Heine-Borel Theorem"

(Statement)
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Revision as of 16:25, 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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