From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5156 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: 'Directed Algebraic Topology' Date: Mon, 21 Sep 2009 11:56:47 -0400 (EDT) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1253552769 22773 80.91.229.12 (21 Sep 2009 17:06:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 21 Sep 2009 17:06:09 +0000 (UTC) To: Urs Schreiber , categories@mta.ca Original-X-From: categories@mta.ca Mon Sep 21 19:05:59 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MpmKH-0008PF-7e for gsmc-categories@m.gmane.org; Mon, 21 Sep 2009 19:05:21 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Mply1-0004D6-7j for categories-list@mta.ca; Mon, 21 Sep 2009 13:42:21 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5156 Archived-At: One obvious thing that comes to mind are asymmetric spaces--a metric=20 without the symmetry axiom. This can obviously be extended to uniform=20 spaces, although I am not aware anyone has. As for topological spaces, I= =20 know of nothing there. Michael On Mon, 21 Sep 2009, Urs Schreiber wrote: > Marco Grandis wrote: > >> My book >> >> =A0 =A0'Directed Algebraic Topology' >> =A0 =A0Models of non-reversible worlds >> >> has appeared, at Cambridge University Press. > > In that context I am wondering about the following: > > it would be nice to have a notion of directed topological space that > would extend the relation between (nice) topological spaces and > oo-groupoids to one between (nice) directed topological spaces and > (oo,1)-categories. > > More generally, it would be nice to have a notion of "r-directed > topological space" for r in N that would extend the relation between > (nice) topological spaces and oo-groupoids to one of (nice) > "r-directed spaces" and (oo,r)-cateories. > > (Probably such a notion of directed spaces can't be supporrted by > plain topological spaces with direction information, but requires > filtered directed spaces or the like. ) > > Has anything like this been considered? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]