From: Rainer Vogt <Rainer.Vogt@mathematik.Uni-Osnabrueck.DE>
Date: Fri, 22 Jan 1999 16:42:23 +0100 (MET)
Subject: Re: associativity


>
> Date: Mon, 18 Jan 1999 15:01:29 -0500 (EST)
> From: Michael Cole <mmcole@math.lsa.umich.edu>
> Subject: point set trivia
>
> As long as we're discussing basepoints, I have a simple question about
> smash products.  In the category of based k spaces one easily proves that
> the smash product is associative using the fact that the compactly
> generated product preserves proclusions.  I have heard it said that the
> category of all based topological spaces is not symmetric monoidal under
> the smash product since the smash product is not associative.  What is the
> simplest example of nonassociativity?
>
> Mike Cole
>

There is a counterexample to associativity in Puppe's article in Math.
Zeitschr. 69 (1958) p. 336: (Q smash Q) smash N is not homeomorphic to
Q smash (Q smash N) where Q is the space of rationals and N is the natural
numbers.

Rainer Vogt