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Prove or disprove: A countably infinite intersection of compact sets is compact. Show that if a set of real numbers A is connected, then for

Prove or disprove: A countably infinite intersection of compact sets is compact.

Show that if a set of real numbers A is connected, then for any closed sets X, Y C A such that X, Y # A and XnY = 0 we have XUY # A

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