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    Connected Convex Subsets

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    Let A and B be separated subsets of some Rk, suppose and , and define

    for . Put , . [Thus if and only if .]

    (a) Prove that Ao and Bo are separated subsets of R1 .
    (b) Prove that there exists such that .
    (c) Prove that every convex subset of Rk is connected

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    https://brainmass.com/math/geometry-and-topology/connected-convex-subsets-169659

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    Let A and B be separated subsets of some Rk, suppose and , and define

    for . Put , . [Thus if and only if .]

    (a) Prove that Ao and Bo are separated subsets of R1 .
    (b) Prove that there exists such that .
    (c) Prove ...

    Solution Summary

    Connected convex subsets are investigated.

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