Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 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 non-homeomophic 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

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