Talk:Uniform space

Of hundreds of mathematical projects which I could do this one is the least attactive. Somehow, with little prompting :-), I got stuck with it. So be it.

to do

The article gets a bit big, and the number of issues is growing. Thus let me make a list of things to do. Once they are on record, they will not get forgotten.

• Check the Aleksandrov-Urysohn metrization paper; they got a characterization essentially in the uniform terms (as I remember). Also find the pre-Smimrnov name of the original Soviet author of the nearness relation (Efimov? Efremenko? E...?).
• Show that open entourages for a uniform base.
• Generating a uniform structure by a family of uniform structures; it is applied especially to families of pseudometrics.
• Write a bit more of the category stuff (the forgetful functors).

These are the gaps in the present version, to be filled up. Of course several topics should be added:

• Compact spaces.
• Completeness and completions.
• Ascoli-Arzela.
• Mention topological groups.

Wlodzimierz Holsztynski 02:55, 20 December 2007 (CST)

Names, history

It was Efremovich. I have several refences. I need to relearn how to insert them into a wiki text. My references come from the Russian translations of Bourbaki and Kelly. In both cases P.S> Aleksandrov wrote introductions. In the latter case there are also footnotes made by the translator, A.Archangielski. I am not hundered percent sure which of the brothers Riesz was mentioned by Aleksandrov (he didn't bother to provide the iinitial of the first name), but I am pretty confident that it was the older of the two brothers, i.e. Frigyes Riesz (rather than Marcel Riesz).