Talk:Separable space: Difference between revisions
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Why "separable"? What's being separated? Is it something like, e.g., a rational number separates any two real numbers? [[User:BenFrantzDale|—Ben FrantzDale]] 23:42, 25 October 2006 (UTC) |
Why "separable"? What's being separated? Is it something like, e.g., a rational number separates any two real numbers? [[User:BenFrantzDale|—Ben FrantzDale]] 23:42, 25 October 2006 (UTC) |
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These two properties are a bit unclear: |
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* Every second-countable space is separable. |
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* A metric space is separable if and only if it is second-countable and if and only if it is Lindelöf. |
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Clearly a MS is a space so if separable iff second countable; so should the second one not be |
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In a Metric space the following are equivalent: |
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-- space 2nd countable |
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-- space separable |
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-- space Lindelof |
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This is not an edit as I would need to check first in Kelley. |
Revision as of 11:23, 18 April 2007
This needs to be merged with separable space. Charles Matthews
(This has been done.)
Hi Fropuff,
I do not think your condensing made the article clearer. You removed my introduction sentence where I tried to give an intuitive explanation for the laymen (or not topologist) in terms of approximation. Furthermore although the ==Definition== section was quite short it was nonetheless useful for the reader as he could immediatly jump the the definition of the concept without scanning the whole article.
Your other edits , especially on the properties I added, are an improvement and made the article clearer.MathMartin 12:21, 6 Mar 2005 (UTC)
Hmm, User:Charles Matthews's edits made my points above somewhat moot. I still would like to see the definition separated out into a ==Definition== section but now I can live with the page. MathMartin 13:20, 6 Mar 2005 (UTC)
Sorry, I hadn't really looked at what changes you'd made before I made mine. In most cases I would agree with you regarding the definition section, however, in this case I think the definition is short enough and clear enough that it doesn't hurt to include it in the first sentence. -- Fropuff 15:36, 2005 Mar 6 (UTC)
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Why "separable"? What's being separated? Is it something like, e.g., a rational number separates any two real numbers? —Ben FrantzDale 23:42, 25 October 2006 (UTC)
These two properties are a bit unclear:
- Every second-countable space is separable.
- A metric space is separable if and only if it is second-countable and if and only if it is Lindelöf.
Clearly a MS is a space so if separable iff second countable; so should the second one not be
In a Metric space the following are equivalent:
-- space 2nd countable -- space separable -- space Lindelof
This is not an edit as I would need to check first in Kelley.