quasi
Posts:
11,910
Registered:
7/15/05


Re: Stone Cech
Posted:
Mar 21, 2013 4:03 AM


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.
quasi

