quasi
Posts:
10,741
Registered:
7/15/05


Re: Stone Cech
Posted:
Mar 21, 2013 6:21 AM


quasi wrote: >quasi wrote: >>quasi wrote: >>>Butch Malahide wrote: >>>>David C. Ullrich wrote: >>>>>Butch Malahide wrote >>>>> >William Elliot wrote: >>>>> >>David Hartley wrote: >>>>> >> >William Elliot wrote: >>>>> >> >> >>>>> >> >>Perhaps you could illustrate with the five different >>>>> >> >>one to four point point compactifications of two open >>>>> >> >>end line segements. >>>>> >> > >>>>> >> > (There are seven.) >>>>> >> >>>>> >> Ok, seven nonhomeomophic finite Hausdorff compactications. >>>>> > >>>>> >How many will there be if you start with n segments instead >>>>> >of 2? >>>>> >>>>> Surely there's no simple formula for that? >>>>> >>>>> ... >>>> >>>> ... >>>> >>>>I wasn't necessarily expecting a *complete* answer, such as an >>>>explicit generating function. Maybe someone could give a partial >>>>answer, such as an asymptotic formula, or nontrivial upper and >>>>lower bounds, or a reference to a table of small values, or the >>>>ID number in the Encyclopedia of Integer Sequences, or just the >>>>value for n = 3. (I got 21 from a hurried hand count.) >>> >>>For n = 3, my hand count yields 19 distinct compactifications, >>>up to homeomorphism. >>> >>>Perhaps I missed some cases. >> >>I found 1 more case. >> >>My count is now 20. > >I found still 1 more case. > >So 21 it is! > >But after that, there are no more  I'm certain.
Oops  the last one I found was bogus.
So my count is back to 20.
quasi

