et X be a metric space with metric d. Let r > 0 and define the open ball center at EX with radius r >0 by B,(x) = {y € X : d(x,y) < r}. et {BCX:(Vro E B), (3r10 > 0), such that B, (ro) C B}. Show that T is a topology in X and Show that B,(x) is open set with respect to T for allr>0

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