From: Pedro Resende <firstname.lastname@example.org>
To: Steven Vickers <email@example.com>
Cc: categories list <firstname.lastname@example.org>
Subject: categories: Re: Terminology for point-free topology?
Date: Fri, 27 Jan 2023 17:55:38 +0000 [thread overview]
Message-ID: <E1pLVkO-0001Xo-2E@rr.mta.ca> (raw)
Sorry for the radio silence, it’s been a hectic week.
Concerning your question about a less derogatory expression… I think I like `algebraic reasoning’ versus `point-based reasoning’ (which to me sounds better than `pointwise', I don’t 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’ 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.
> On Jan 23, 2023, at 1:47 PM, Steven Vickers <email@example.com> wrote:
> 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,
> From: firstname.lastname@example.org > Sent: Monday, January 23, 2023 11:44 AM
> To: email@example.com <mailto:firstname.lastname@example.org> <email@example.com <mailto:firstname.lastname@example.org>>
> Cc: Steven Vickers (Computer Science) <email@example.com <mailto:firstname.lastname@example.org>>; categories list <email@example.com <mailto:firstname.lastname@example.org>>
> 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… :)
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next prev parent reply other threads:[~2023-01-27 20:55 UTC|newest]
Thread overview: 19+ messages / expand[flat|nested] mbox.gz Atom feed top
2023-01-16 11:50 Steven Vickers
[not found] ` <email@example.com>
2023-01-18 12:12 ` Steven Vickers
2023-01-20 3:06 ` David Yetter
[not found] ` <SN6PR05MB5213EBE225CB83D101EA0F57A2C59@SN6PR05MB5213.namprd05.prod.outlook.com>
2023-01-20 11:50 ` Steven Vickers
2023-01-21 19:42 ` ptj
2023-01-23 11:44 ` Pedro Resende
2023-01-30 21:59 ` categories: " Wesley Phoa
2023-02-01 9:41 ` Martin Hyland
[not found] ` <18E1AA5F-0054-4CA3-B231-BD9B799B03A2@tecnico.ulisboa.pt>
2023-01-23 13:47 ` Steven Vickers
[not found] ` <YQXPR01MB26464DF33EAE7481847A4F82E5C99@YQXPR01MB2646.CANPRD01.PROD.OUTLOOK.COM>
2023-01-24 12:20 ` categories: " Robert Pare
2023-01-27 17:55 ` Pedro Resende [this message]
2023-01-28 5:43 ` Patrik Eklund
2023-01-29 23:16 ` dawson
2023-01-28 10:48 ` categories: complete Galois groups Clemens Berger
2023-01-30 17:34 ` categories: " Eduardo J. Dubuc
[not found] ` <LNXP265MB1049E00AEC9CE5BE1233CCEF95C69@LNXP265MB1049.GBRP265.PROD.OUTLOOK.COM>
2023-01-22 21:32 ` Terminology for point-free topology? Vaughan Pratt
[not found] ` <CAL7kZqCz081nyFQuo_QFfaGzGe+UBORJHOZWsO9VgNzpDJ9_Gw@mail.gmail.com>
2023-01-23 13:25 ` Steven Vickers
[not found] ` <LNXP265MB104912A7940157738582CE2595C89@LNXP265MB1049.GBRP265.PROD.OUTLOOK.COM>
2023-01-23 23:17 ` categories: " Vaughan Pratt
[not found] ` <CAL7kZqAPzmzf=wt=qKNBjjeb_dGtG4eDu7tv5Eku-AVZD7wWtw@mail.gmail.com>
2023-01-24 11:45 ` Steven Vickers
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