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Let (X,d) be a metric space which contains an infinite countable set Ewith the property x,y...

  1. Let (X,d) be a metric space which contains an infinite countable set Ewith the property x,y ∈ E ⇒ d(x,y) = 1.

    (a) Show E is a closed and bounded subset of X. (b) Show E is not compact.

    (c) Explain why E cannot be a subset of Rn for any n.

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