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- Questione Show Mebnc space (d) is. that show then closed ball Y in clasead set Alsa complete is d) is completeShow that the space P is complete.Let X be a topological space. Show that the following are equivalent. (i) X is disconnected. (ii) 3 a nonempty proper subset of X which is both open and closed in X.
- The intersection of any countable family of open dense - sets in a locally compact space X is dense.Let R, S, and T be sets. Let f: R -» S, and g: S -» T be maps. Assume we know that qf is 1-1 Must f be 1-1? Either prove that it is or find a counterexample (a) Must g be 1-1? Either prove that it is or find a counterexample (b)Let X And Y be two distrecte spaces. Then X is homeomorphic to Y if and only if X and Y are both infinite?