Talk:Uniform space: Difference between revisions

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imported>Hendra I. Nurdin
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imported>Wlodzimierz Holsztynski
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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 group]]s.
[[User:Wlodzimierz Holsztynski|Wlodzimierz Holsztynski]] 02:55, 20 December 2007 (CST)

Revision as of 02:55, 20 December 2007

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 Definition:  Topological space with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence. [d] [e]
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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:

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

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