SOLVED: Prove that every nonempty proper subset of a connected space has a nonempty boundary. Is the converse also true? Let X be a connected metric space with an unbounded metric d. Prove that the set y | d(r,y) = r is nonempty for each x ∈ X. Is this also true when X is disconnected?
SOLVED: Prove that every nonempty proper subset of a conn…
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