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Prove that a subspace of R is compact if and only if it is closed...

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Advance Math

Prove that a subspace of R is compact if and only if it is closed and bounded.

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4.3 Ratings (1113 Votes)
An unbounded subset of R has an open cover consisting of all bounded open intervals This has no finite subcover since the union of a finite set of bounded intervals is bounded Similarly if K is not closed then it has a boundary point x K But then the collec tion of    See Answer
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