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From: Jeff Smith <jhs@math.purdue.edu>
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
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> 
> 
> 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