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William Elliot wrote:
> ---- From: rusty <mr.rusty@xxxxxxx>
> Newsgroups: sci.math
> Subject: Re: Complete metric quotient spaces
>
> William Elliot wrote:
>
>> You gradually seem to be working out what a Polish space is ;-)
>
> A Polish space is any space homeomorphic to a complete metric space?
separable
> Why's it called Polish? Because Bourbaki were Polish?
I will let you guess. There is probably a historical appendix in Bourbaki's
General Topology.
I think that Jacques Dixmier was the member of the Bourbaki group
responsable for this chapter. Often people first come across this work by
reading George Mackey and others who followed in his path like James Glimm,
Michael Fell and Calvin Moore, one of the great US promoters of Polish
spaces.
The only volume of Bourbaki I possess is Chapters IV-VI of Lie groups and
algebras (in french of course), one of the greatest mathematics books of
all time. It was probably written by Serre with help from Tits and others.
It has an excellent historical appendix.
>
>> >> <news:4506cb3b$0$11850$636a55ce@xxxxxxxxxxxx>
>>
>> > [Malformed "news" URL: Invalid newsgroup specified]
>>
>> >> <news:4507c708$0$11852$636a55ce@xxxxxxxxxxxx>
>>
>> > [Malformed "news" URL: Invalid newsgroup specified]
>
>> What else do you expect if you use Pine? The recommended way to
>> access messages like this from Pine is to enter the Message-Id in the
>> message box here:
>
>> http://groups.google.com/advanced_search
>
> What's the message-id, the part after : and before @ ?
The part after "news:"; Isn't google your friend any more?
>
>> I managed to find the two relevant pages in Bourbaki this way. First
>> I looked in the contents and noted on which pages the results were
>> likely to appear ("quotient spaces" and "Polish spaces"
>> respectively). Then I entered these as search terms and picked out
>> the nearest page. Quite simple. No need to buy the book. I too have
>> Kelley but it's not a useful reference for Polish spaces.
>
> Go Google
books.google.com/">http://books.google.com/
Most educated people seem to know about google books these days.
> on
> Bourbaki, "Topology"
enter "Bourbaki general topology"
> and search document
within the page devoted to Bourbaki's "General Topology"
> for
> quotient spaces
> Polish spaces ?
Yes you put these in the part "search within book"
>
>> > As you see, cancelled messages do get through.
>
>> Pine again ;(
>
> Pardo'n Monsieur, no polyvou France'.
Why do you assume I'm french? Not very intelligent.
Use a proper news reader.
>
>> By the way, how do you cancel messages in Pine?
>
> The old fashiion way,
Did you mean to write "old-fashioned"?
> by proof reading before posting and composing off
> line.
>
Ah, that would account for your odd question about closed G_delta's.
Très drôle.
>> > Kelly claims a G_delta within a complete metric space is
>> > homeomophic to a complete metric space. Gives suggestions how to
>> > construct the homeomorphism.
>
>> The implications in both directions are proved in Bourbaki
>> or Arveson (or probably even in Kuratowski's Topologie).
>
>> G_delta's arise naturally as follows. A group acts on a convex set
>> which also has the structure of a compact metric space. The extreme
>> points form a G_delta on which the group acts. This is therefore
>> equivalent to a group action on a metric space that is complete and
>> separable (i.e. a "complete separable metric space"), in part the
>> subject of this thread.
>
> Kelley's suggestions fail to invoke such strange apparitions.
>
I wish you all the best in your future career outside mathematics.
--
rusty
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