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    Question about Connected point sets

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    Prove whether the following is true or false. If it is false give a counter example.

    If M is a connected point set, the cl(M) is connected.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:37 pm ad1c9bdddf

    Solution Preview

    There is a basic lemma that says: If the sets C and D form a separation of X, and if Y is a connected subset of X, then Y lies entirely within either C or D. Call this "Lemma A".
    Suppose cl(M) is not connected. Then cl(M) = C U D ...

    Solution Summary

    This is a proof regarding connected point sets.