From: Robert Pare <R.Pare@Dal.Ca>
To: "categories@mta.ca" <categories@mta.ca>
Subject: categories: Re: Terminology for point-free topology?
Date: Tue, 24 Jan 2023 12:20:35 +0000 [thread overview]
Message-ID: <E1pKj2t-0002rt-TP@rr.mta.ca> (raw)
In-Reply-To: <YQXPR01MB26464DF33EAE7481847A4F82E5C99@YQXPR01MB2646.CANPRD01.PROD.OUTLOOK.COM>
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/ ]
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<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>
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Dear Steve,</div>
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I've been following this thread with interest, though I've never worked</div>
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on the subject. In trying to understand what it's actually all about, I've</div>
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come to the conclusion that it's "copoint topology". Is that Crazy?</div>
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<br>
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Cheers,</div>
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<br>
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Bob<br>
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<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>
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<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>
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next prev parent reply other threads:[~2023-01-25 16:56 UTC|newest]
Thread overview: 19+ messages / expand[flat|nested] mbox.gz Atom feed top
2023-01-16 11:50 Steven Vickers
[not found] ` <a23cbfc0-7433-eec1-115e-af2041d4cfd1@uu.nl>
2023-01-18 12:12 ` Steven Vickers
2023-01-20 3:06 ` David Yetter
[not found] ` <SN6PR05MB5213EBE225CB83D101EA0F57A2C59@SN6PR05MB5213.namprd05.prod.outlook.com>
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] ` <18E1AA5F-0054-4CA3-B231-BD9B799B03A2@tecnico.ulisboa.pt>
2023-01-23 13:47 ` Steven Vickers
[not found] ` <YQXPR01MB26464DF33EAE7481847A4F82E5C99@YQXPR01MB2646.CANPRD01.PROD.OUTLOOK.COM>
2023-01-24 12:20 ` Robert Pare [this message]
2023-01-27 17:55 ` categories: " 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] ` <CAL7kZqCz081nyFQuo_QFfaGzGe+UBORJHOZWsO9VgNzpDJ9_Gw@mail.gmail.com>
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] ` <CAL7kZqAPzmzf=wt=qKNBjjeb_dGtG4eDu7tv5Eku-AVZD7wWtw@mail.gmail.com>
2023-01-24 11:45 ` Steven Vickers
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