On Wed, 21 May 2003, Andy Latto wrote:
-----Original Message----- From: John McCarthy [mailto:jmc@steam.Stanford.EDU] Sent: Tuesday, May 20, 2003 7:27 PM To: math-fun@mailman.xmission.com Cc: math-fun@mailman.xmission.com; jmclists@cs.Stanford.EDU Subject: Re: [math-fun] Re: Canonical 1-1 correspondences
John Conway wrote
But if you're going to allow infinite classes, then trivially the set of all correspondences is a canonical one.
Yes, but consider the correspondences between X and X* you get when you choose a basis for X. A basis element b of X corresponds to the functional that is 1 on b and 0 on the other basis elements. It seems to me that these correspondences should be the canonical set of correspondences. However, I don't know of a general criterion for preferring them.
Aren't these exactly the linear bijections between X and X*?
Yes, they are. JHC