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Science Forum Index » Math - Symbolic Forum » quotient space problem...
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| Jan Kubrik... |
 Posted: Tue May 13, 2008 6:08 am |
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Consider R^n with the usual topology and consider an equivalence relation ~ on R^n with classes that consist of 2 and only 2 different elements
(for every x in R^n we have [x]={x,x'}). Is it possible that the quotient space R^n/~ :
i) is Hausdorff,
ii) is indiscrete,
iii) is discrete? |
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| Daniel Lichtblau... |
| Posted: Tue May 13, 2008 6:20 am |
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On May 13, 11:08 am, Jan Kubrik <kubri... at (no spam) gmail.com> wrote:
Quote: Consider R^n with the usual topology and consider an equivalence relation ~ on R^n with classes that consist of 2 and only 2 different elements
(for every x in R^n we have [x]={x,x'}). Is it possible that the quotient space R^n/~ :
i) is Hausdorff,
ii) is indiscrete,
iii) is discrete?
Are they pairing continuously? That usually factors into whether they
are being indiscreet.
As for the rest, what happened last month with this?
http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist;task=show_msg;msg=0857.0001
Daniel Lichtblau
Wolfram Research |
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| Robert H. Lewis... |
| Posted: Tue May 13, 2008 7:41 am |
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Quote: Consider R^n with the usual topology and consider an
equivalence relation ~ on R^n with classes that
consist of 2 and only 2 different elements
(for every x in R^n we have [x]={x,x'}). Is it
possible that the quotient space R^n/~ :
i) is Hausdorff,
ii) is indiscrete,
iii) is discrete?
You seem to have posted to the wrong sci.math group. This is for symbolic computation.
Robert H. Lewis
Fordham University |
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