From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3459 Path: news.gmane.org!not-for-mail From: Paul Taylor Newsgroups: gmane.science.mathematics.categories Subject: Lawvere-metrics and Banach spaces Date: Tue, 17 Oct 2006 11:19:21 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241019317 8839 80.91.229.2 (29 Apr 2009 15:35:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:35:17 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Oct 17 08:25:37 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 17 Oct 2006 08:25:37 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GZn0N-0007M3-4o for categories-list@mta.ca; Tue, 17 Oct 2006 08:21:07 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 21 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:3459 Archived-At: There is a widely cited paper by Bill Lawvere called "Metric spaces, generalised logic and closed catgeories" in which he shows how metric spaces are examples of enriched categories. The enriching structure consists of the nonnegative reals, with "greater than" as the morphisms and addition as the tensor product. Using this one can generalise the notion of metric space by substituting other structures in place of R. An obvious question is - what happens when we follow through this idea for Banach spaces? What becomes of the $\ell_p$ spaces and of dual spaces? Do families of semi-norms naturally fit into this pattern? Paul Taylor