Date: Tue, 19 Jan 1999 01:15:00 -0500 (EST)
From: Tony Elmendorf <aelmendo@math.purdue.edu>
Subject: basepoint reply

My thanks to those who answered my query.  Mike Cole's response is wrong:
let S be the set {0} U {1/n: n>0}.  The reduced cone on S is a quotient
of S x I.  Then the map S x I ---> I given by sending (a,b) to ab descends
to a map on the cone which sends only the basepoint to 0.  Then the homotopy
h: S x I x I ---> S x I  sending (a,t,s) to (a, min{t,1-s}) also descends
to a homotopy on the cone exhibiting the baspoint as a deformation retract
of the cone.

Gerd Laures's response is surely correct, but I doubt the space I^M is
compactly generated.  I neglected to mention that I wanted both X and Y
to be compactly generated in my original question.  If we k-ify I^M, is it
still degenerately based?  I don't know the answer.  Anybody?

Tony Elmendorf