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  • Dodging Holes in the Plane

    From William Elliot@21:1/5 to All on Mon Aug 28 07:07:20 2017
    If the union of a countable pairwise disjoint collection of
    bounded, simply connected open sets is removed from the real
    plain, is the result path connected?

    If the union of a countable pairwise disjoint collection of
    simply connected compact sets with non-empty interior, is
    removed from the real plain, is the result path connected?

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  • From Bill@21:1/5 to William Elliot on Mon Aug 28 15:45:04 2017
    William Elliot wrote:

    If the union of a countable pairwise disjoint collection of
    bounded, simply connected open sets is removed from the real
    plain, is the result path connected?

    If the union of a countable pairwise disjoint collection of
    simply connected compact sets with non-empty interior, is
    removed from the real plain, is the result path connected?



    I don't know the answers, but I would see if I could use a tool like
    the
    function y=sin(1/x), to achieve a "negative" result. ��"Fun" problem! �
    -Bill

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