Dear Steve, I've been following this thread with interest, though I've never worked on the subject. In trying to understand what it's actually all about, I've come to the conclusion that it's "copoint topology". Is that Crazy? Cheers, Bob ________________________________ From: Steven Vickers <s.j.vickers.1@bham.ac.uk> Sent: January 23, 2023 9:47 AM To: categories list <categories@mta.ca> Subject: categories: Re: Terminology for point-free topology? 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: pedro.m.a.resende@tecnico.ulisboa.pt <pedro.m.a.resende@tecnico.ulisboa.pt> Sent: Monday, January 23, 2023 11:44 AM To: ptj@maths.cam.ac.uk <ptj@maths.cam.ac.uk> Cc: Steven Vickers (Computer Science) <s.j.vickers.1@bham.ac.uk>; categories list <categories@mta.ca> 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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ] --_000_YQXPR01MB2646265C1D8882E80428F9F5E5C99YQXPR01MB2646CANP_ Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=Windows-1252"> <style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style> </head> <body dir="ltr"> <div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);" class="elementToProof"> <br> </div> <div id="appendonsend"></div> <hr style="display:inline-block;width:98%" tabindex="-1"> <div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Robert Pare <R.Pare@Dal.Ca><br> <b>Sent:</b> January 24, 2023 8:19 AM<br> <b>To:</b> Steven Vickers <s.j.vickers.1@bham.ac.uk><br> <b>Cc:</b> categories@mta <categories@mta><br> <b>Subject:</b> Re: categories: Re: Terminology for point-free topology?</font> <div> </div> </div> <style type="text/css" style="display:none"> <!-- p {margin-top:0; margin-bottom:0} --> </style> <div dir="ltr"> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> Dear Steve,</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> <br> </div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> I've been following this thread with interest, though I've never worked</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> on the subject. In trying to understand what it's actually all about, I've</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> come to the conclusion that it's "copoint topology". Is that Crazy?</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> <br> </div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> Cheers,</div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> <br> </div> <div class="x_elementToProof" style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0); background-color:rgb(255,255,255)"> Bob<br> </div> <div id="x_appendonsend"></div> <hr tabindex="-1" style="display:inline-block; width:98%"> <div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Steven Vickers <s.j.vickers.1@bham.ac.uk><br> <b>Sent:</b> January 23, 2023 9:47 AM<br> <b>To:</b> categories list <categories@mta.ca><br> <b>Subject:</b> categories: Re: Terminology for point-free topology?</font> <div> </div> </div> <div class="x_BodyFragment"><font size="2"><span style="font-size:11pt"> <div class="x_PlainText">CAUTION: The Sender of this email is not from within Dalhousie.<br> <br> Dear Pedro,<br> <br> Of course, that's the very reason why I wanted to transfer it to the style of working without points.<br> <br> 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.<br> <br> 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.<br> <br> Do you think there's a less derogatory term for the style of reasoning without points?<br> <br> All the best,<br> <br> Steve.<br> <br> ________________________________<br> From: pedro.m.a.resende@tecnico.ulisboa.pt <pedro.m.a.resende@tecnico.ulisboa.pt><br> Sent: Monday, January 23, 2023 11:44 AM<br> To: ptj@maths.cam.ac.uk <ptj@maths.cam.ac.uk><br> Cc: Steven Vickers (Computer Science) <s.j.vickers.1@bham.ac.uk>; categories list <categories@mta.ca><br> Subject: Re: categories: Re: Terminology for point-free topology?<br> <br> 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… :)<br> <br> Pedro<br> <br> <br> [For admin and other information see: <a href="http://www.mta.ca/~cat-dist/">http://www.mta.ca/~cat-dist/</a> ]<br> </div> </span></font></div> </div> </body> </html> --_000_YQXPR01MB2646265C1D8882E80428F9F5E5C99YQXPR01MB2646CANP_-- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]