Subject: Answer for the mailing list
Date: Thu, 13 Nov 2003 15:30:06 +0100
From: Gaucher Philippe <gaucher@pps.jussieu.fr>
Organization: PPS
To: Don Davis <dmd1@lehigh.edu>

Le Jeudi 13 Novembre 2003 14:06, vous avez écrit :

> I hope this answers the question that was being asked by Philippe
> Gaucher:
>
> If  i:A ---> X  is a cofibration, then so is (Id,i):YxA-->YxX  for any
> space  Y.

I hope I am not making myself another confusion... It seems that you are
making a confusion between Serre cofibration (a cofibration for the Quillen
model structure) and Hurewicz cofibration (a closed map satisfying the
homotopy extension property).

In the language of model category, what you are saying is that any space is
cofibrant with the Strom model structure. The latter model structure is
monoidal, so indeed, (Id,i):YxA-->YxX is always a Hurewicz cofibration as
soon as A-->X is a Hurewicz cofibration.

This was not my question. I was talking about a Serre cofibration A-->X, that
is a cofibration for the Quillen model structure on CGTop.

Anyway, I found an answer for my question by adapting the proof of the left
properness of the Quillen model category of topological spaces.

pg.