We say that a subset C of a metric space X is closed if its complement...

 

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We say that a subset C of a metric space X is closed if its complement XIC is open. Show that if xo EX and r 20, then D-(x) = {x EX | d(x, xo) ≤r}CX is a closed set. We call this the closed ball of radius r about xo. We say that a subset C of a metric space X is closed if its complement XIC is open. Show that if xo EX and r 20, then D-(x) = {x EX | d(x, xo) ≤r}CX is a closed set. We call this the closed ball of radius r about xo.

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