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Robert Israel wrote:
In article <Pine.BSI.4.58.0609140326310.7806@xxxxxxxxxxxxxxxxx>,
William Elliot <marsh@xxxxxxxxxxxxxxxxxx> 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?
You left out separable.
Why's it called Polish? Because Bourbaki were Polish?
Bourbaki were mostly French. Sierpinski, Kuratowski, Tarski, Banach etc.
were Polish.
As I recall, wasn't Polish space originally called "Name" space, where
"Name" was the name of a Polish mathematician? I thought that some non
Polish speaker found the name hard to pronounce, so s/he came up with
the more simply pronounced term, "Polish space."
When I first encountered Polish spaces (named for the person, I think),
IIRC, they were defined as topological spaces with a list of certain
properties. It was then a theorem that a topological space is Polish if
and only if it is separable and metrizable to be complete.
My memory may very well be wrong on both these counts. Wikipedia
disagrees with me. (Kind of like dairy products.)
--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan
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