Date: Fri, 18 Aug 2000 15:36:09 -0400 (EDT)
From: "Haynes Miller" <hrm@math.mit.edu>

I wanted to check it because of the thread about groups which can
be homotopy groups, to see if anyone had pointed to


89g:55021 Shelah, Saharon Can the fundamental (homotopy) group of a
space be the rationals? Proc. Amer. Math. Soc. 103
(1988), no. 2, 627--632. (Reviewer: Andreas Blass) 55Q05 (03E15 03E40)


in which

"The author proves that, for any path-connected, locally path-connected,
compact metric space, the fundamental group is either finitely
generated or of the cardinality of the continuum."


haynes