< October 10 | << Sep | October | Nov>> | October 12 > |
---|
| ||||||||
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions at one of the pages linked to above. | ||||||||
This may be a little advanced for this page, but I'll give it a shot anyway. Does anyone know of an example of a topological group which is connected but not path-connected? Or do such groups not exist? Of course, such a group cannot be locally path connected and so cannot be anything nice like a Lie group. -- Fropuff 17:59, 11 October 2006 (UTC)
Consider in RxR, with the usual topology, X={(x,sin(1/x)) | x is in [1,0)}, and Y={(0,y) | y in [-1.1]}, now, XUY is connected and not path-connected. By the way, it is not an advanced topic.
Right :P, sorry my wrong
I do not believe such groups exist. Google doesn't seem to be coming up with either a proof or a counterexample, so I'd try Bourbaki next.
RandomP 18:47, 11 October 2006 (UTC)
Okay, I have a nice answer compliments of Daniel Asimov (who responded to a question posted on sci.math.research by Rich). The p-adic solenoid is a compact, connected abelian topological group which is neither path-connected nor locally-connected. I have yet to work out what the path component of the identity is, or the group of path components, but at least I have something to play with. -- Fropuff 06:36, 18 October 2006 (UTC)
Given the uselessly slow loading of images (including TeX) the last few days (at least sporadically), it seems practical to find other wiki sites that are fully TeX supported (and with open preview privileges) to work on articles (some, like
http://uncyclopedia.org, seem to support most TeX, but not the most recent commands/effects——e.g., "{\color{white}.}V=Q", to add a hidden character for space value at the beginning). Anyone know of any alternate sites to use for such purposes?
~Kaimbridge~
19:14, 11 October 2006 (UTC)
Just hit the "Random page" link, then the "edit": Blank out the text that is there, cut and paste whatever you are working on, work on it, then cut it back out and save it wherever you had it before (you are just "previewing" on uncyclopedia, not saving anything).
Okay, after you landed on the "cooking page", you should have hit the "edit" link at the top, deleted the text, then work on whatever. The wiki TeX endmarkers
are "<math>" and "</math>" (not "$"s) and the negative space is "\!", so a small space ("\,") and a negative space cancel out: Using your example, the proper way to format a fraction is "<math>V=\frac{N}{D}\,\!</math>", which should come out as .
There is a good "cheat sheet" page,
Help:Formula (though I prefer an
older version, as the format layout is better——besides using the "printable yes" link). P=)
~Kaimbridge~
14:13, 13 October 2006 (UTC)
It's not a matter of forcing TeX to activate, but recognizing the initial character/command as spacing (it ignores it):
Is there a better way?
~Kaimbridge~
10:08, 12 October 2006 (UTC)
< October 10 | << Sep | October | Nov>> | October 12 > |
---|
| ||||||||
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions at one of the pages linked to above. | ||||||||
This may be a little advanced for this page, but I'll give it a shot anyway. Does anyone know of an example of a topological group which is connected but not path-connected? Or do such groups not exist? Of course, such a group cannot be locally path connected and so cannot be anything nice like a Lie group. -- Fropuff 17:59, 11 October 2006 (UTC)
Consider in RxR, with the usual topology, X={(x,sin(1/x)) | x is in [1,0)}, and Y={(0,y) | y in [-1.1]}, now, XUY is connected and not path-connected. By the way, it is not an advanced topic.
Right :P, sorry my wrong
I do not believe such groups exist. Google doesn't seem to be coming up with either a proof or a counterexample, so I'd try Bourbaki next.
RandomP 18:47, 11 October 2006 (UTC)
Okay, I have a nice answer compliments of Daniel Asimov (who responded to a question posted on sci.math.research by Rich). The p-adic solenoid is a compact, connected abelian topological group which is neither path-connected nor locally-connected. I have yet to work out what the path component of the identity is, or the group of path components, but at least I have something to play with. -- Fropuff 06:36, 18 October 2006 (UTC)
Given the uselessly slow loading of images (including TeX) the last few days (at least sporadically), it seems practical to find other wiki sites that are fully TeX supported (and with open preview privileges) to work on articles (some, like
http://uncyclopedia.org, seem to support most TeX, but not the most recent commands/effects——e.g., "{\color{white}.}V=Q", to add a hidden character for space value at the beginning). Anyone know of any alternate sites to use for such purposes?
~Kaimbridge~
19:14, 11 October 2006 (UTC)
Just hit the "Random page" link, then the "edit": Blank out the text that is there, cut and paste whatever you are working on, work on it, then cut it back out and save it wherever you had it before (you are just "previewing" on uncyclopedia, not saving anything).
Okay, after you landed on the "cooking page", you should have hit the "edit" link at the top, deleted the text, then work on whatever. The wiki TeX endmarkers
are "<math>" and "</math>" (not "$"s) and the negative space is "\!", so a small space ("\,") and a negative space cancel out: Using your example, the proper way to format a fraction is "<math>V=\frac{N}{D}\,\!</math>", which should come out as .
There is a good "cheat sheet" page,
Help:Formula (though I prefer an
older version, as the format layout is better——besides using the "printable yes" link). P=)
~Kaimbridge~
14:13, 13 October 2006 (UTC)
It's not a matter of forcing TeX to activate, but recognizing the initial character/command as spacing (it ignores it):
Is there a better way?
~Kaimbridge~
10:08, 12 October 2006 (UTC)