A subset A of M is said to be nowhere dense if int(A) = 0. Prove...

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A subset A of M is said to be nowhere dense if int(A) = 0. Prove that {x} is nowhere dense if and only if x is not an isolated point of M! Recall that a point is isolated from a set if there exists an open ball containing it that is not intersecting with that particular set. A subset A of M is said to be nowhere dense if int(A) = 0. Prove that {x} is nowhere dense if and only if x is not an isolated point of M! Recall that a point is isolated from a set if there exists an open ball containing it that is not intersecting with that particular set.

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To prove that z is nowhere dense if and only if z is not an isolated point of M we need to sh... View the full answer