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- Show that any finite union of Nowhere Dense Sets is Nowhere Dense.We say that a space (X, τ) is not connected if there exist two nonempty openings A, B such that A ∩ B = ∅ and A ∪ B = X. A space (X, τ) isconnected if it does not meet the previous condition. Show that if the only subsets that are both open and closed are X and ∅ then the space is connected.Let X And Y be two distrecte spaces. Then X is homeomorphic to Y if and only if X and Y are both infinite?