From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10910 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Pedro Resende Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology for point-free topology? Date: Mon, 23 Jan 2023 11:44:47 +0000 Message-ID: References: Reply-To: Pedro Resende Mime-Version: 1.0 (Mac OS X Mail 13.4 \(3608.120.23.2.7\)) Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="37799"; mail-complaints-to="usenet@ciao.gmane.io" To: categories list Original-X-From: majordomo@rr.mta.ca Mon Jan 23 23:18:24 2023 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.75]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1pK58w-0009UV-UW for gsmc-categories@m.gmane-mx.org; Mon, 23 Jan 2023 23:18:23 +0100 Original-Received: from rr.mta.ca ([198.164.44.159]:39570) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pK58U-0008Kw-DG; Mon, 23 Jan 2023 18:17:54 -0400 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pK57j-00046C-UW for categories-list@rr.mta.ca; Mon, 23 Jan 2023 18:17:07 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10910 Archived-At: 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 :) Pedro > On Jan 21, 2023, at 7:42 PM, ptj@maths.cam.ac.uk wrote: >=20 > 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'. >=20 > 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. >=20 > Peter Johnstone >=20 > On Jan 21 2023, Steven Vickers wrote: >=20 >> Dear David, >>=20 >> Yes, and it's an excellent paper with a witty title for which only >> "pointless" would do. >>=20 >> 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". >>=20 >> He went on to say, >>=20 >> "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." >>=20 >> 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. >>=20 >> 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.) >>=20 >> Best wishes, >>=20 >> Steve. >>=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]