From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10911 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Steven Vickers Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology for point-free topology? Date: Mon, 23 Jan 2023 13:47:00 +0000 Message-ID: References: Reply-To: Steven Vickers Mime-Version: 1.0 Content-Type: text/plain; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="9520"; mail-complaints-to="usenet@ciao.gmane.io" To: categories list Original-X-From: majordomo@rr.mta.ca Mon Jan 23 23:20:29 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 1pK5Az-00026P-HH for gsmc-categories@m.gmane-mx.org; Mon, 23 Jan 2023 23:20:29 +0100 Original-Received: from rr.mta.ca ([198.164.44.159]:39592) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pK5AY-0000G1-Sm; Mon, 23 Jan 2023 18:20:02 -0400 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pK59e-00048a-EG for categories-list@rr.mta.ca; Mon, 23 Jan 2023 18:19:06 -0400 In-Reply-To: <18E1AA5F-0054-4CA3-B231-BD9B799B03A2@tecnico.ulisboa.pt> Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10911 Archived-At: 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, w= ithout 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 a= re 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 with= out points? All the best, Steve. ________________________________ 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) ; categorie= s list Subject: Re: categories: Re: Terminology for point-free topology? In addition to all the deeper reasons, `pointless=92 can be taken to be der= ogatory, so preferably it should be used only when in tongue-in-cheek mode.= At least that=92s what I tell my students =97 just as I ask them not to sa= y `abstract nonsense=92 too enthusiastically=85 :) Pedro [For admin and other information see: http://www.mta.ca/~cat-dist/ ]