From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: * X-Spam-Status: No, score=1.2 required=5.0 tests=DATE_IN_PAST_24_48, LOCALPART_IN_SUBJECT,RCVD_IN_MSPIKE_H2 autolearn=no autolearn_force=no version=3.4.4 Received: (qmail 22543 invoked from network); 25 Jan 2023 16:56:05 -0000 Received: from smtp2.mta.ca (198.164.44.75) by inbox.vuxu.org with ESMTPUTF8; 25 Jan 2023 16:56:05 -0000 Received: from rr.mta.ca ([198.164.44.159]:39936) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pKj3z-0001dO-PL; Wed, 25 Jan 2023 12:55:55 -0400 Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pKj2t-0002rt-TP for categories-list@rr.mta.ca; Wed, 25 Jan 2023 12:54:47 -0400 From: Robert Pare To: "categories@mta.ca" Subject: categories: Re: Terminology for point-free topology? Date: Tue, 24 Jan 2023 12:20:35 +0000 References:

In-Reply-To: Accept-Language: en-CA, en-US Content-Language: en-CA Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Precedence: bulk Reply-To: Robert Pare Message-Id: Dear Steve, I've been following this thread with interest, though I've never worked on the subject. In trying to understand what it's actually all about, I've come to the conclusion that it's "copoint topology". Is that Crazy? Cheers, Bob ________________________________ From: Steven Vickers Sent: January 23, 2023 9:47 AM To: categories list Subject: categories: Re: Terminology for point-free topology? 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, w= ithout 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 a= re much more purely algebraic gadgets. Our approach via localic suplattices= (algebras for the lower hyperspace monad) gives a more point-free approac= h to the subject, but it takes effort - I think you'll agree - to work wit= h the hyperspaces in a pointwise manner. Do you think there's a less derogatory term for the style of reasoning with= out points? All the best, Steve. ________________________________ From: pedro.m.a.resende@tecnico.ulisboa.pt Sent: Monday, January 23, 2023 11:44 AM To: ptj@maths.cam.ac.uk Cc: Steven Vickers (Computer Science) ; categorie= s list Subject: Re: categories: Re: Terminology for point-free topology? In addition to all the deeper reasons, `pointless=92 can be taken to be der= ogatory, so preferably it should be used only when in tongue-in-cheek mode.= At least that=92s what I tell my students =97 just as I ask them not to s= ay `abstract nonsense=92 too enthusiastically=85 :) Pedro [For admin and other information see: http://www.mta.ca/~cat-dist/ ] --_000_YQXPR01MB2646265C1D8882E80428F9F5E5C99YQXPR01MB2646CANP_ Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable

From: Robert Pare <R.Par= e@Dal.Ca>
Sent: January 24, 2023 8:19 AM
To: Steven Vickers <s.j.vickers.1@bham.ac.uk>
Cc: categories@mta <categories@mta>
Subject: Re: categories: Re: Terminology for point-free topology?

Dear Steve,

I've been following this thread with interest, though I've never worked

on the subject. In trying to understand what it's actually all about, I've<= /div>

come to the conclusion that it's "copoint topology". Is that Craz= y?

Cheers,

Bob

From: Steven Vickers <= s.j.vickers.1@bham.ac.uk>
Sent: January 23, 2023 9:47 AM
To: categories list <categories@mta.ca>
Subject: categories: Re: Terminology for point-free topology?

CAUTION: The Sender of this email is not from wi= thin Dalhousie.

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, w= ithout 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 a= re much more purely algebraic gadgets. Our approach via localic suplattices= (algebras for the lower hyperspace monad) gives a more point-free ap= proach to the subject, but it takes effort - I think you'll agree - to work with the hyperspaces in a pointwis= e manner.

Do you think there's a less derogatory term for the style of reasoning with= out points?

All the best,

Steve.

________________________________
From: pedro.m.a.resende@tecnico.ulisboa.pt <pedro.m.a.resende@tecnico.ul= isboa.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>; cat= egories list <categories@mta.ca>
Subject: Re: categories: Re: Terminology for point-free topology?

In addition to all the deeper reasons, `pointless=92 can be taken to be der= ogatory, so preferably it should be used only when in tongue-in-cheek mode.= At least that=92s what I tell my students =97 just as I ask them not= to say `abstract nonsense=92 too enthusiastically=85 :)

Pedro

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

--_000_YQXPR01MB2646265C1D8882E80428F9F5E5C99YQXPR01MB2646CANP_-- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]