topol. separation axiom T_0
Bernd Baumgarten
Recently, I asked:
>
> in a paper I am writing, I talk about topological T0-spaces
> (Kolmogorov-spaces). I took the definition from a German book.
> However, the paper being in English, I would rather like to cite
> an English language text book. Kelley and Dugundji do not mention T0!
> Does anyone know a "standard" text defining T0/Kolmogorov?
>
> Please e-mail.
>...
> -----
> Bernd Baumgarten, GMD, Rheinstr. 75, D-64295 Darmstadt, Germany
> Tel. +49 6151 869263, Fax +49 6151 869224, baum...@darmstadt.gmd.de
I should definitely have asked more precisely:
** Which generally available English language textbook defines
** T0-spaces and calls them Kolmogorov?
** ----------
** (Kelley and Dugundji do not mention Kolmogorov.
** ----------
That's why the T_0 exercise in Kelley wouldn't do ...
Thanks for the pointers to it! Sorry that I took your time.
For reasons of mere curiosity, it would be even greater also to know
why on earth "Kolmogorov"! Of course, he was/is famous, but
I guess his name was not chosen accidentally.
Did he define them first, or some precursor version of them?
Regards,
Bernd
PS:
In case you want to know why I don't just use "T_0" in my paper:
I found T_0 very important in a generalization of topology,
and I want to extend T_0 to that generalization. However,
my paper is intended for an audience most of whom do not care
about topology. So I want to avoid "T_0", because it would, all
alone, look somewhat unmotivated to non-topologists.
(Why T_0? What about T_(some other number)?")
Ilias Kastanas
In article <baumgart-0...@i2rh-mac110.darmstadt.gmd.de>,
Bernd Baumgarten <baum...@darmstadt.gmd.de> wrote:
>Recently, I asked:
>>
>> in a paper I am writing, I talk about topological T0-spaces
>> (Kolmogorov-spaces). I took the definition from a German book.
>> However, the paper being in English, I would rather like to cite
>> an English language text book. Kelley and Dugundji do not mention T0!
>> Does anyone know a "standard" text defining T0/Kolmogorov?
>>
>> Please e-mail.
>>...
>> -----
>> Bernd Baumgarten, GMD, Rheinstr. 75, D-64295 Darmstadt, Germany
>> Tel. +49 6151 869263, Fax +49 6151 869224, baum...@darmstadt.gmd.de
>
>I should definitely have asked more precisely:
>
>** Which generally available English language textbook defines
>** T0-spaces and calls them Kolmogorov?
>** ----------
>** (Kelley and Dugundji do not mention Kolmogorov.
>** ----------
>
>That's why the T_0 exercise in Kelley wouldn't do ...
>Thanks for the pointers to it! Sorry that I took your time.
>
>For reasons of mere curiosity, it would be even greater also to know
>why on earth "Kolmogorov"! Of course, he was/is famous, but
>I guess his name was not chosen accidentally.
>Did he define them first, or some precursor version of them?
Kuratowski ("Topology", vol. I, p. 51) attributes T_0 to
Kolmogorov, and gives as reference Alexandroff-Hopf.
Ilias