Subject: Re: 5 questions and job
Date: Mon, 15 Oct 2001 12:53:16 -0400 (EDT)
From: Walter Neumann <neumann@math.columbia.edu>
To: Don Davis <dmd1@lehigh.edu>

On Mon, 15 Oct 2001, Don Davis wrote:

> Subject: question for list
> Date: Fri, 12 Oct 2001 21:30:02 -0400
> From: Tom Goodwillie <tomg@math.brown.edu>
>
> The following question came up in my topology class:
>
> If two retractions from X to A are homotopic, are they
> necessarily homotopic through retractions?
>
> The answer is "yes" if the pair (X,A) has the homotopy extension
> property, and I'm guessing that it's "no" in general, but I
> haven't come up with a counterexample.
>
> Tom Goodwillie
> ____________________________

I think $X = R \times \{0\} \cup Q \times [0,1]$,
$A=\{(x,y)\in X : x\ge 0\}$
$f(x,y)= (|x|,y) $
$g(x,y)=(2|x|-x,y) $
might do it.

--walter neumann