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Union of closed intervals

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Reference no: EM131703313

Prove that any open cover of R (real numbers) has an at most countable subcover.

For this proof, my professor wants us to go in this direction: Show that R can be written as the union of closed intervals, and since closed intervals are compact, each interval has an open cover which admits a finite subcover. Then, a finite union of subcovers covers R.

Reference no: EM131703313

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