quasi
Posts:
12,067
Registered:
7/15/05


Re: Stone Cech
Posted:
Mar 21, 2013 5:35 AM


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.
quasi

