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| Started by | William Elliot <marsh@panix.com> |
|---|---|
| First post | 2016-04-08 10:31 -0600 |
| Last post | 2016-04-10 05:56 -0600 |
| Articles | 5 — 3 participants |
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Pesky Connection William Elliot <marsh@panix.com> - 2016-04-08 10:31 -0600
Re: Pesky Connection David Cullen <davecullen@gmail.com> - 2016-04-09 18:24 -0600
Re: Pesky Connection William Elliot <marsh@panix.com> - 2016-04-10 05:54 -0600
Re: Pesky Connection Robin Chapman <R.J.Chapman@exeter.ac.uk> - 2016-04-10 05:55 -0600
Re: Pesky Connection David Cullen <davecullen@gmail.com> - 2016-04-10 05:56 -0600
| From | William Elliot <marsh@panix.com> |
|---|---|
| Date | 2016-04-08 10:31 -0600 |
| Subject | Pesky Connection |
| Message-ID | <080420161031244853%edgar@math.ohio-state.edu.invalid> |
Let (S,d) a multi-point connected metric space. Is there a multi-point path connected subspace of S?
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| From | David Cullen <davecullen@gmail.com> |
|---|---|
| Date | 2016-04-09 18:24 -0600 |
| Message-ID | <090420161824054572%edgar@math.ohio-state.edu.invalid> |
| In reply to | #1968 |
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?
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| From | William Elliot <marsh@panix.com> |
|---|---|
| Date | 2016-04-10 05:54 -0600 |
| Message-ID | <100420160554364766%edgar@math.ohio-state.edu.invalid> |
| In reply to | #1969 |
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 ]
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| From | Robin Chapman <R.J.Chapman@exeter.ac.uk> |
|---|---|
| Date | 2016-04-10 05:55 -0600 |
| Message-ID | <100420160555418657%edgar@math.ohio-state.edu.invalid> |
| In reply to | #1969 |
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?
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| From | David Cullen <davecullen@gmail.com> |
|---|---|
| Date | 2016-04-10 05:56 -0600 |
| Message-ID | <100420160556512876%edgar@math.ohio-state.edu.invalid> |
| In reply to | #1969 |
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?
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