Subject: Question for Toplist
Date: Tue, 17 Sep 2002 16:12:53 -0400 (EDT)
From: Claude Schochet <claude@math.wayne.edu>

Suppose that G is a separable metric topological group (probably not
compact) which has the homotopy type of a CW complex. In
addition, each homotopy group of G is countable. (In the examples I'm
thinking of \pi _n = \pi _{n+2}, so there are an infinite number of
non-zero homotopy groups).

What does one have to assume about G in order to conclude that

a)      G has the homotopy type of a countable CW complex

b)      G has the homotopy type of a CW complex of finite type

c)      G is of the rational homotopy type of a product of
        Eilenberg-MacLane spaces.

Thanks!

Claude