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

  • Pesky Connection

    From William Elliot@21:1/5 to All on Fri Apr 8 10:31:24 2016
    Let (S,d) a multi-point connected metric space.
    Is there a multi-point path connected subspace of S?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From David Cullen@21:1/5 to William Elliot on Sat Apr 9 18:24:05 2016
    William Elliot <marsh@panix.com> wrote:

    Let (S,d) a multi-point connected metric space.
    Is there a multi-point path connected subspace of S?

    Can you provide the definition of multipoint connected?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From William Elliot@21:1/5 to David Cullen on Sun Apr 10 05:54:36 2016
    David Cullen <davecullen@gmail.com> wrote:

    William Elliot <marsh@panix.com> wrote:

    Let (S,d) a multi-point connected metric space.
    Is there a multi-point path connected subspace of S?

    Can you provide the definition of multipoint connected?

    Let (S,d) a multi-point connected metric space.
    Is there a multi-point path connected subspace of S?

    Can you provide the definition of multipoint connected?

    Multipoint mean has more than one point.
    Connected means there are no clopen sets but
    the empty set and the space itself.

    As it turns out, Cantor's leaky tent or teepee
    in Stien's "Counterexamples in Topology". is
    an example negating the question.

    [
    Moderator's note:
    Steen & Seebach
    ]

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Robin Chapman@21:1/5 to David Cullen on Sun Apr 10 05:55:41 2016
    David Cullen <davecullen@gmail.com> wrote:

    William Elliot <marsh@panix.com> wrote:

    Let (S,d) a multi-point connected metric space.
    Is there a multi-point path connected subspace of S?

    Can you provide the definition of multipoint connected?


    I presume that William's question amounts to the following:
    does a connected metric space with more than one point
    necessarily have a path-connected subset with more than
    one point?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From David Cullen@21:1/5 to All on Sun Apr 10 05:56:51 2016
    Ok if you are asking if there is an example of a metric space which is connected, and at the same time is also totally path disconnected, then
    I suspect the knaster-kuratowski fan space will suffice.  It is known
    to be connected, and I suspect it is totally path disconnected as well,
    though I haven't done the legwork yet. Does this work?

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