Q:Find two disjoint clsed subsets of (R^2) which are zero distance a part? my answer is A & B where A={(1/n) : n belong to z+}X{0} B={[-1,0]XR} Is it right
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No, it is not correct. Notice that . So , and this set is not closed since is a boundary point not in . However, consider the sets and .
Originally Posted by hatsoff However, consider the sets and . Thank u for your respond but looks like is not closed since is boundry point for the set C which not conained in D. Am I right or wrong
D is a set, not a point. So D could not possibly *be* a boundary point. Think of it graphically: C is just the curve y=1/x in the first quadrant of the plane. D is the line y=0.
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