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From: rusty <mr.rusty@xxxxxxx>
Newsgroups: sci.math
Subject: Re: Complete metric quotient spaces
> This time you have replied to a message posted at 13:40 and cancelled at
> 13:44 yesterday. Please see the two subsequent posts. By the way (0,1)
is
> a Polish space since it is homeomorphic to the complete metric space
> (-\infty, \infty). I suggest you look up the references in Chapter IX of
> Bourbaki's General Topology for your own eduaction. And no I do not mean
a
> closed G_delta. Please see my two other messages and please check
> carefully before replying to a cancelled message.
(0,1) is not a complete metric space by the definition
every Cauchy sequence converges to a point.
However with a topologically equivalent, but not uniformly equivalent
metric, (0,1) can be mapped to R which is complete.
Cancelled messages will show up without any indication.
Please proof read your posts before sending.
> If you can't find them on your news reader the other two messages
> are:
I've one, more thought out, post or yours yet to download and read.
I read and compose off line for stuff that requires good answers.
For hot shot stuff, I flip it off, on line. As it was, I downloaded
three of your hastily written posts and answered them when I was
intending to download the one with substance. Oh well, I'll get to
it tomorrow.
> <news:4506cb3b$0$11850$636a55ce@xxxxxxxxxxxx>
[Malformed "news" URL: Invalid newsgroup specified]
> <news:4507c708$0$11852$636a55ce@xxxxxxxxxxxx>
[Malformed "news" URL: Invalid newsgroup specified]
> I have just noticed your strange comments and the extraordinary way
> you have edited/rearranged/concatenated some of my previous posts. I
> see you do not understand the definition of a Polish space. As for
> algebras, have you heard of the Stone-Weierstrass theorem or the
> Gelfand-Naimark correspondence?
No.
> My use of the term algebra is current amongst professional
> mathematicians: I'm sorry if you were unaware of this.
The uses of algebra I'm familiar with relate to vector spaces
and measure theory.
> Why did you delete the first reference to the result on quotients
> of compact metric spaces from Bourbaki's General Topology?
Beyond my reach.
> As for your "no do have" concerning Bourbaki, if you are not near a
> mathematics library or do not possess this book (as I was yesterday
> afternoon), you can find all the relevant pages on google books by
> an intelligent use of search terms within the book.
No I'm not near a univerisy library and I've little success with google
books unless your suggesting I buy a copy. That I can do thru Powell's
Books and have Kelley's 'General Topology' and Steen's 'Counterexamples in
Topology'.
> In addition I have checked your statement about cancelled messages
> using two news readers on accounts outside France (pmms.cam.ac.uk
> and math.berkeley.edu) and I am unable to confirm what you wrote.
As you see, cancelled messages do get through.
> I wish you luck with Bourbaki.
Kelly claims a G_delta within a complete metric space is homeomophic to a
complete metric space. Gives suggestions how to construct the
homeomorphism.
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