Re: Another question on Grothendieck

[Steven Vickers <S.J.Vickers@cs.bham.ac.uk>]

Dear Eduardo,

I have written papers that deliberately have two possible meanings: one
classical point-set and one constructive point-free.

That is to say, the development in terms of points is done under logical
(geometric) constraints that enable it to be interpreted in topos-valid
point-free topology (locales), but it can be interpreted directly in
point-set topology if one accepts classical logic.

I did this for expositional reasons, to help classical topologists
understand the topological content of what I was doing.

See:

   "Localic completion of generalized metric spaces I"
   "The connected Vietoris powelocale"

Is this compatible with what you were saying about "only one possible
meaning"?

Regards,

Steve Vickers.

On Fri, 03 Sep 2010 22:03:19 -0300, "Eduardo J. Dubuc" <edubuc@dm.uba.ar>
wrote:
> I confess that I am a little bit confused about what Vaughan is saying.
> 
> This promps me to repeat my posting in other words:
> 
> If a mathematical statement is understood by a reader (the hypotesis,
> the conclusion and the proof)
> 
> then the mathematical meaning of any particular notation used should
> come up by itself to this reader (that is, it should be clear for him
> that only one possible meaning for this particular notation would make
> the things work).
> 
> Eduardo

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