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...?).

Done. Wlodzimierz Holsztynski 15:30, 27 December 2007 (CST)

• Show that open entourages for a uniform base.

Done. Wlodzimierz Holsztynski 15:30, 27 December 2007 (CST)

• 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.

Partially done (to be continued). Wlodzimierz Holsztynski 15:30, 27 December 2007 (CST)

• 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). Wlodzimierz Holsztynski 21:37, 21 December 2007 (CST)

Length

I feel that each article in citizendium should be interesting on its own, that no article should be auxiliary only. For this reason I am not splitting the Uniform space into subartciles. I don't feel that a chapter of "uniform space" would be interesting by itself. If there is an iinteresting special subtopic then sure, let it fill a separate article.

Thus this article is long and is going to be still longer. I wish, the segment before "Contents" were editable by itself. When an article is long then it is a pain to have the whole article in the editing window instead of the top segment only. This is why I prefer, against the wiki common customs, to name the top segment like any other, say "Introduction"; but I am going along the consensus (and against my better judgement :-). Wlodzimierz Holsztynski 17:09, 26 December 2007 (CST)

Actually, there can be a separate article Uniform compact space, and another about Uniform Arzela-Ascoli theorem. On the topological side there can be the respective Topological Arzela-Ascoli theorem. Wlodzimierz Holsztynski 04:26, 27 December 2007 (CST)

to do, cnt.

I still need to add more material about complete and compact spaces. But first I have to write about the constructions and operations on uniform spaces, so that I can talk about subspaces, gauge spaces, etc. Wlodzimierz Holsztynski 17:13, 26 December 2007 (CST)