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Topic: Stone Cech
Replies: 49   Last Post: Mar 28, 2013 12:15 PM

 Messages: [ Previous | Next ]
 Butch Malahide Posts: 894 Registered: 6/29/05
Re: Stone Cech
Posted: Mar 23, 2013 2:52 AM

On Mar 22, 10:27 pm, Butch Malahide <fred.gal...@gmail.com> wrote:
> On Mar 22, 10:52 am, David C. Ullrich <ullr...@math.okstate.edu>
> wrote:
>
>
>
>
>

> > I just realized I have no idea whatever how to write
> > a correct algorithm here, even without worrying

>
> > An equivalence relation on the 2n endpoints
> > determines a compactification. It also determines
> > a graph, where the vertices are the equivalence
> > classes of endpoints and the edges are the
> > original segments. Earlier, thinking that I was
> > thinking about deciding when two of these
> > compactifications are homeomorphic, I was
> > actually thinking about how to determine
> > whether two of the graphs are isomorphic.
> > That's a strictly weaker condition... I have
> > no idea how I'd check whether two equivalences
> > gave homeomorphic compactifications.

>
> You mean, non-isomorphic is a weaker condition than non-homeomorphic.
>
> The remedy for that is to stick to graphs with no vertices of degree
> 2. (OK, you have to make an exception for the graph consisting of a
> single vertex of degree 2, corresponding to the one-point
> compactification of R.)

Oops, I was thinking of connected graphs. In general, you want to work
with graphs with the property that any vertex of degree 2 is the only
vertex in its component. OK, so you have graphs G and H that you want
to test for homeomorphism. Remove vertices of degree 2 (and unify the
two edges that were incident with that vertex) until you get graphs G'
and H', homeomorphic to G and H respectively (G and H are subdivisions
of G' and H') and having the aforesaid property; and then test G' and
H' for isomorphism. So homeomorphism testing (of graphs) is no harder
than isomorphism testing.

Date Subject Author
3/14/13 William Elliot
3/14/13 fom
3/15/13 fom
3/16/13 William Elliot
3/15/13 David C. Ullrich
3/17/13 William Elliot
3/17/13 David C. Ullrich
3/17/13 fom
3/18/13 David C. Ullrich
3/18/13 fom
3/18/13 David Hartley
3/19/13 William Elliot
3/19/13 David Hartley
3/19/13 William Elliot
3/20/13 Butch Malahide
3/20/13 David C. Ullrich
3/20/13 Butch Malahide
3/20/13 Butch Malahide
3/21/13 quasi
3/21/13 quasi
3/21/13 quasi
3/21/13 quasi
3/21/13 Butch Malahide
3/21/13 quasi
3/22/13 Butch Malahide
3/22/13 Butch Malahide
3/22/13 Butch Malahide
3/22/13 quasi
3/22/13 David C. Ullrich
3/22/13 David C. Ullrich
3/22/13 Butch Malahide
3/23/13 Butch Malahide
3/23/13 David C. Ullrich
3/23/13 David C. Ullrich
3/23/13 Frederick Williams
3/23/13 David C. Ullrich
3/23/13 Frederick Williams
3/22/13 Butch Malahide
3/23/13 David C. Ullrich
3/22/13 Butch Malahide
3/23/13 quasi
3/23/13 Butch Malahide
3/23/13 Butch Malahide
3/24/13 quasi
3/24/13 Frederick Williams
3/24/13 quasi
3/25/13 Frederick Williams
3/28/13 Frederick Williams
3/25/13 quasi
3/19/13 David C. Ullrich