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Topic: Totally bounded uniform spaces vs proximity spaces (need proof)
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Victor Porton

Posts: 529
Registered: 8/1/05
Totally bounded uniform spaces vs proximity spaces (need proof)
Posted: Mar 7, 2014 3:44 PM
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At

http://math.stackexchange.com/questions/694365/totally-bounded-uniform-spaces-vs-proximity-spaces-need-proof

I've formulated this question:

nLab says "The category of totally bounded uniform spaces
and uniformly continuous functions is equivalent to the
category of proximity spaces and proximally continuous
functions":

http://ncatlab.org/nlab/show/totally+bounded+space

How to prove this? Maybe, I already have a general topology
book with this proof? Both answers with references and
(better) answers with a complete proof are appreciated.

My conversation about this follows:

http://ncatlab.org/nlab/show/proximity+space in the sector
uniform spaces, actually sketches the proof...
? Henno Brandsma Feb 28 at 20:47

@HennoBrandsma: I haven't yet understood, why "These sets
form a base for a totally bounded uniformity on X" at
http://ncatlab.org/nlab/show/proximity+space

--
Victor Porton - http://portonvictor.org



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