Talk:Separable space

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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)

[edit] Name

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)

[edit] Properties

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.

Alanb 11:23, 18 April 2007 (UTC)

[edit] "non-separable Hilbert spaces in theoretical physics" - TWO COMMENTS.

This concerns the statement: "The possible use of non-separable Hilbert spaces in theoretical physics has provoked some inconclusive debate."

(1) Can someone expand further on this cryptic comment, perhaps citing a reference where one can learn more?

(2) I was a little disturbed to find that Google knows about just two sites that have the phrase "non-separable Hilbert spaces in theoretical physics": this site (this wikipedia page) and the following .com site:

 http://www.nationmaster.com/encyclopedia/Separable-space

Who has borrowed this intellectual content from whom? I suppose in the end there is nothing to be done...

DrTLesterThomas (talk) 23:07, 9 June 2008 (UTC)