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).

I also have Russian tranlations of the Urysohn works, including the joint Aleksandrov-Urysohn papers (but in Russian).