From jhs@math.purdue.edu Fri Feb 4 14:05:23 2000 Return-Path: Received: from newton.math.purdue.edu (root@newton.math.purdue.edu [128.210.3.6]) by nss4.cc.lehigh.edu (8.9.3/8.9.3) with ESMTP id OAA70962 for ; Fri, 4 Feb 2000 14:05:22 -0500 Received: from hille.math.purdue.edu (jhs@hille.math.purdue.edu [128.210.3.222]) by newton.math.purdue.edu (8.9.3/8.9.3/PURDUE_MATH-3.3) with ESMTP id OAA12157 for ; Fri, 4 Feb 2000 14:05:21 -0500 (EST) Received: (from jhs@localhost) by hille.math.purdue.edu (8.9.3/8.9.3/PURDUE_MATH-3.2) id OAA16664 for dmd1@lehigh.edu; Fri, 4 Feb 2000 14:05:18 -0500 (EST) From: Jeff Smith Message-Id: <200002041905.OAA16664@hille.math.purdue.edu> Subject: Re: response re delta sets To: dmd1@lehigh.edu (DON DAVIS) Date: Fri, 4 Feb 2000 14:05:18 -0500 (EST) In-Reply-To: <200002031924.OAA45398@ns1-1.CC.Lehigh.EDU> from "DON DAVIS" at Feb 03, 2000 02:24:26 PM X-Mailer: ELM [version 2.5 PL0] MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit > > > One comment, the CW-complexes that arise as the geometric realization of a > Delta set are the same CW-complexes that arise as the geometric realization > of a simplicial set. In fact there is a functor sending the the Delta set > X to the simplicial set sX such that the geometric realization of the Delta > set X is the same CW-complex as the geometric realization of the siplicial set > sX. > > Geometrically there is no difference between Delta sets and > simplicial sets. > > > Jeff Smith > > A comment on my comment. The last sentence is nonsense. It has to do with my own bias. I find Delta sets to be ugly and was hoping for a reason to ignore them. If I were forced to use them I would regard Delta sets as a special kind of simplicial set; Delta sets are a full subcategory of simplicial sets. Jeff Smith