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=-0.0 required=5.0 tests=RCVD_IN_MSPIKE_H2 autolearn=ham autolearn_force=no version=3.4.4 Received: (qmail 32163 invoked from network); 27 Jan 2023 20:55:46 -0000 Received: from smtp2.mta.ca (198.164.44.75) by inbox.vuxu.org with ESMTPUTF8; 27 Jan 2023 20:55:46 -0000 Received: from rr.mta.ca ([198.164.44.159]:40226) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pLVl6-0005ti-1r; Fri, 27 Jan 2023 16:55:40 -0400 Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pLVkO-0001Xo-2E for categories-list@rr.mta.ca; Fri, 27 Jan 2023 16:54:56 -0400 From: Pedro Resende MIME-Version: 1.0 (Mac OS X Mail 13.4 \(3608.120.23.2.7\)) Subject: categories: Re: Terminology for point-free topology? Date: Fri, 27 Jan 2023 17:55:38 +0000 Cc: categories list To: Steven Vickers References: Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset="utf-8" Precedence: bulk Reply-To: Pedro Resende Message-Id: Hi Steve, Sorry for the radio silence, it=E2=80=99s been a hectic week. Concerning your question about a less derogatory expression=E2=80=A6 I = think I like `algebraic reasoning=E2=80=99 versus `point-based = reasoning=E2=80=99 (which to me sounds better than `pointwise', I = don=E2=80=99t know why). This is analogous to commutative algebra versus algebraic geometry. In any case, am I right that it seems to be somewhat consensual (in this = thread) that `pointfree topology=E2=80=99 is the appropriate terminology = for the kind of topology that *can* (but not necessarily has to) be = studied without reasoning in terms of points? Incidentally, in my mind the `pointfree' terminology should also apply = to more general notions, such as quantales, or at least some classes of = them. For instance, inverse quantal frames are `the same' as localic = etale groupoids, and they have associated etendues. Best wishes, Pedro > On Jan 23, 2023, at 1:47 PM, Steven Vickers = wrote: >=20 > Dear Pedro, >=20 > Of course, that's the very reason why I wanted to transfer it to the = style of working without points. >=20 > 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. >=20 > 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. >=20 > Do you think there's a less derogatory term for the style of reasoning = without points? >=20 > All the best, >=20 > Steve. >=20 > 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) >; categories list > > Subject: Re: categories: Re: Terminology for point-free topology? > =20 > In addition to all the deeper reasons, `pointless=E2=80=99 can be = taken to be derogatory, so preferably it should be used only when in = tongue-in-cheek mode. At least that=E2=80=99s what I tell my students = =E2=80=94 just as I ask them not to say `abstract nonsense=E2=80=99 too = enthusiastically=E2=80=A6 :) >=20 > Pedro [For admin and other information see: http://www.mta.ca/~cat-dist/ ]