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From: Pedro Resende <>
To: Steven Vickers <>
Cc: categories list <>
Subject: categories: Re: Terminology for point-free topology?
Date: Fri, 27 Jan 2023 17:55:38 +0000	[thread overview]
Message-ID: <> (raw)
In-Reply-To: <>

Hi Steve,

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.

Best wishes,


> On Jan 23, 2023, at 1:47 PM, Steven Vickers <> 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,
> Steve.
> From: > Sent: Monday, January 23, 2023 11:44 AM
> To: <> < <>>
> Cc: Steven Vickers (Computer Science) < <>>; categories list < <>>
> 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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  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] ` <>
2023-01-18 12:12   ` Steven Vickers
2023-01-20  3:06     ` David Yetter
     [not found]     ` <>
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]     ` <>
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] ` <>
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] ` <>
2023-01-24 11:45   ` Steven Vickers

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