quasi
Posts:
10,833
Registered:
7/15/05


Re: Stone Cech
Posted:
Mar 21, 2013 4:26 AM


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.
quasi

