Talk:Uniform space

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There was a second definition that was basically a corrupt variation of the definition of a proximity space. Although there is a close relationship between proximity and uniformity, the two are distinct notions.

I added the second definition thinking poximinity was the same concept as uniformity. The last few days I tried unsucessfully to prove this or find any reference. Thanks for fixing it. Can you point me to any reference on proximity space ? MathMartin 10:54, 24 Feb 2005 (UTC)

I will be adding references to the proximity space page.--192.35.35.35 13:38, 24 Feb 2005 (UTC)

The term for something satisfying the first four entourage axioms is "quasiuniformity".--192.35.35.34 15:25, 23 Feb 2005 (UTC)

Yes you are correct, I meant to write quasiuniformity.MathMartin 10:54, 24 Feb 2005 (UTC)

This is in line with "quasimetric" and "quasiproximity".--192.35.35.35 13:38, 24 Feb 2005 (UTC)

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The Notes section, with the translation of the axioms one by one, is silly. Is there a reader who actually finds it helpful to be walked through all five translations? The result, to me, is far more confusing.--192.35.35.34 16:47, 23 Feb 2005 (UTC)

A one by one translation is probably not useful but generally there should be a note explaining the idea behind the definition.MathMartin 10:54, 24 Feb 2005 (UTC)

OK, I'll be rewriting it. I wanted to be bold and just change it first, but seeing how long it has been part of the article, I didn't want to ruffle any feathers.--192.35.35.35 13:38, 24 Feb 2005 (UTC)

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Why is Steen & Seebach in the references?--192.35.35.34 16:57, 23 Feb 2005 (UTC)

I added the reference, but it can be removed. MathMartin 10:54, 24 Feb 2005 (UTC)

I'll be adding some more uniform space specific references.--192.35.35.35 13:38, 24 Feb 2005 (UTC)

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OK, I think my changes have been for the better. I plan to add material on pseudometric families, total boundedness, Cauchy completeness.--192.35.35.34 16:27, 24 Feb 2005 (UTC)

[edit] Something fishy about the entourage definition

So which is the entourage, Φ or the elements of Φ? The wording suggests that it's the elements of Φ, but then the definition of entourage imposes requirements on Φ, not just on its elements. If the elements of Φ are called entourages, what is Φ itself called? "Set of entourages" seems insufficiently specific. What if you have distinct Φ and Φ', each satisfying the axioms, and you take some elements of each to form a third set Φ₃ that doesn't satisfy the axioms? Isn't it also a set of entourages? All its elements are entourages. --Trovatore 1 July 2005 01:31 (UTC)

Found my answer in the topology glossary, and fixed the article (probably was just a typo) --Trovatore 1 July 2005 02:02 (UTC)