Prove that an open subspace of a locally compact

Reference no: EM132888623

Problem 1: Prove that an open subspace of a compact Hausdorff space is locally compact.

Problem 2: Prove that an open subspace of a locally compact Hausdorff space is locally compact. (Hint: The easy way to do this part is to figure out how to use part (a).)

Problem 3: Suppose that X and Y are metric spaces and view X x Y as a metric space equipped with some good metric. Further suppose that f : X -> Y is a continuous function and consider the graph of f, which is the subspace Γf := {(x, f(x)) : x ∈ X} of X x Y. Prove that Γf. is homeomorphic to X.

Reference no: EM132888623

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