From: Jeff Smith <jhs@math.purdue.edu>
Subject: Re: delta sets
Date: Thu, 3 Feb 2000 14:10:20 -0500 (EST)

>
> Date: Fri, 28 Jan 2000 14:50:49 -0500 (EST)
> From: Allen Hatcher - Math Prof <hatcher@math.cornell.edu>

> Subject: Delta set terminology
>
>      Here's a comment for the discussion list:
>
> Concerning the Delta set terminology: A related issue is what to call the
> geometric incarnations of Delta sets. These are CW complexes with special
> structure. In Brayton Gray's book they are called "semisimplicial CW
> complexes." Does anyone know of other names in the literature?
>
> These geometric objects occur rather often in the algebraic topology
> textbook I'm writing, so I wanted a shorter name and chose to call them
> "Delta complexes" since they are somewhere between simplicial complexes
> and CW complexes, and they are logically the same as Rourke and
> Sanderson's Delta sets. I hope the new terminology doesn't muddy the
> waters too much. In any event, the geometric concept seems extremely
> useful as well as natural, so it deserves to have its own name, and this
> is my candidate.
>
> Allen Hatcher
>


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