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

 Messages: [ Previous | Next ]
 quasi Posts: 12,067 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 non-homeomophic finite Hausdorff compactications.

>>>>> >
>>>>> >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

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