1. Forum
  2. Usenet
  3. SCI.MATH.RESEARCH

  • 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?

    ---

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • 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

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)