Re: Terminology for point-free topology?

[Steven Vickers <s.j.vickers.1@bham.ac.uk>]

Dear Pedro,

Of course, that's the very reason why I wanted to transfer it to the style of working without points.

That's slightly unfair, in that in many cases of reasoning algebraically, without points, it's not at all clear how to do it pointwise.

You and I have certainly experienced that in our work on quantales, which are much more purely algebraic gadgets. Our approach via localic suplattices  (algebras for the lower hyperspace monad) gives a more point-free approach  to the subject, but it takes effort - I think you'll agree - to work with the hyperspaces in a pointwise manner.

Do you think there's a less derogatory term for the style of reasoning without points?

All the best,

Steve.

________________________________
From: pedro.m.a.resende@tecnico.ulisboa.pt <pedro.m.a.resende@tecnico.ulisboa.pt>
Sent: Monday, January 23, 2023 11:44 AM
To: ptj@maths.cam.ac.uk <ptj@maths.cam.ac.uk>
Cc: Steven Vickers (Computer Science) <s.j.vickers.1@bham.ac.uk>; categories list <categories@mta.ca>
Subject: Re: categories: Re: Terminology for point-free topology?

In addition to all the deeper reasons, `pointless’ can be taken to be derogatory, so preferably it should be used only when in tongue-in-cheek mode.  At least that’s what I tell my students — just as I ask them not to say `abstract nonsense’ too enthusiastically… :)

Pedro


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