Subject: Re: question and job
Date: Fri, 7 Nov 2003 14:31:18 -0500
From: Allen Hatcher
To: Don Davis
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.
Namely:
1) A cofibration is always an inclusion of a subspace.
2) A pair (X,A) satisfies the homotopy extension property if and only
if X x I retracts onto (A x I) U (X x {0}).
3) If X x I retracts onto (A x I) U (X x {0}) then X x Y x I
retracts onto (A x Y x I) U (X x Y x {0}) in the obvious way.
If a reference for these elementary facts is wanted, item 1) is proved
on page 460 of my Algebraic Topology book, and 2) is on page 14.
Allen Hatcher