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Science Forum Index » Mathematics Forum » nowhere dense real subsets
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| William Elliot |
 Posted: Sat Dec 27, 2003 12:53 pm |
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If A is a nowhere dense subset of the reals R,
then A is countable.
What's an efficient proof for that theorem?
By efficient I suppose I mean useful to help
find a way of proving the conjecture:
If A is a nowhere dense subset of a
separable compact connected Hausdorff Baire space
is A countable?
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| Rob Johnson |
| Posted: Sat Dec 27, 2003 12:53 pm |
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In article <20031227095100.F31829@agora.rdrop.com>,
William Elliot <marsh@privacy.net> wrote:
Quote: If A is a nowhere dense subset of the reals R,
then A is countable.
What's an efficient proof for that theorem?
By efficient I suppose I mean useful to help
find a way of proving the conjecture:
If A is a nowhere dense subset of a
separable compact connected Hausdorff Baire space
is A countable?
The Cantor set is a nowhere dense set with the cardinality of the reals.
Rob Johnson <rob@trash.whim.org>
take out the trash before replying |
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| Rainer Rosenthal |
| Posted: Sat Dec 27, 2003 6:08 pm |
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Rob Johnson wrote
Quote: The Cantor set ... take out the trash
Hmmm... a nice way of defining it :-)
Rainer Rosenthal
r.rosenthal@web.de |
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| The World Wide Wade |
| Posted: Sat Dec 27, 2003 10:14 pm |
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In article <20031227095100.F31829@agora.rdrop.com>,
William Elliot <marsh@privacy.net> wrote:
Quote: If A is a nowhere dense subset of the reals R,
then A is countable.
That's impressive eggnog you're drinking. |
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| William Elliot |
| Posted: Sun Dec 28, 2003 3:20 am |
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From: Rob Johnson <rob@trash.whim.org>
Subject: Re: nowhere dense real subsets
William Elliot <marsh@privacy.net> wrote:
Quote: If A is a nowhere dense subset of the reals R,
then A is countable.
What's an efficient proof for that theorem?
By efficient I suppose I mean useful to help
find a way of proving the conjecture:
If A is a nowhere dense subset of a
separable compact connected Hausdorff Baire space
is A countable?
The Cantor set is a nowhere dense set
with the cardinality of the reals.
A most efficient proof. ;-)
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