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From: Pedro Resende <>
To: categories list <>
Subject: Re: Terminology for point-free topology?
Date: Mon, 23 Jan 2023 11:44:47 +0000	[thread overview]
Message-ID: <> (raw)
In-Reply-To: <>

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… :)


> On Jan 21, 2023, at 7:42 PM, wrote:
> I was wondering how long it would be before someone in this thread
> referred to my `point of pointless topology' paper! Perhaps not so many
> people know that the title was a conscious echo of an earlier paper
> by Mike Barr called `The point of the empty set', which began with the
> words (I quote from memory) `The point is, there isn't any point there;
> that's exactly the point'.
> As Steve says, to fit that title I had to use the word `pointless', but
> on the whole I prefer `pointfree'; it carries the implication that you
> are free to work without points or to use them (in a generalized sense),
> as you prefer.
> Peter Johnstone
> On Jan 21 2023, Steven Vickers wrote:
>> Dear David,
>> Yes, and it's an excellent paper with a witty title for which only
>> "pointless" would do.
>> I particularly like what Peter said when explaining the significant
>> difference in the absence of choice (such as in toposes of sheaves), and
>> that "usually it is locales, not spaces, which provide the right context
>> in which to do topology".
>> He went on to say,
>> "This is the point which ... Andre Joyal began to hammer home in the
>> early 1970s; I can well remember how, at the time, his insistence that
>> locales were the real stuff of topology, and spaces were merely figments
>> of the classical mathematician's imagination, seemed (to me, and I
>> suspect to others) like unmotivated fanaticism. I have learned better
>> since then."
>> This is all part of the argument for using a reformed topology, but there
>> is nothing particular there about the pointwise style of reasoning for
>> it. Hence we are still left with the question of how to reference the two
>> concepts, the reformed topology and the reasoning without points.
>> Would you call Ng's paper with me pointless? Points are everywhere in it.
>> (Of course, there's the separate issue of whether it was pointless in the
>> sense of not worth the trouble. But an important feature of the style is
>> that it forces you to be careful to distinguish between Dedekind reals
>> and 1-sided (lower or upper) reals, and in Ng's thesis this uncovered
>> unexpected roles of 1-sided reals in the account of Ostrowski's Theorem
>> and the Berkovich spectrum. So there is a bit of payoff.)
>> Best wishes,
>> Steve.

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  reply	other threads:[~2023-01-23 11:44 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 [this message]
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
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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