If a set K that is a subset of the real numbers is closed and bounded,...

If a set K that is a subset of the real numbers is closed and bounded, then it is compact.

Expert Solution

Let K be a closed and bounded subset of real numbers. Then K can be put inside a closed bounded interval [a,b] and we know that closed subset of compact sets are compact. So it is sufficient to prove that closed bounded intervals are compact.

Colby Messinger answered 2 years ago

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