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Prove the following stronger variant of Proposition 7.4. Suppose C is collection of connected subsets of...

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Advance Math

Prove the following stronger variant of Proposition 7.4. SupposeC is collection of connected subsets of a metric space X and B ? C.Show, if for each A ? C, A ? B not equal ?, then ? = ?{C : C ? C}is connected. [Suggestion: Consider the collection D = {C ? B : C ?C}].

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