Date: Sat, 17 Jan 1998 19:21:53 -0500 (EST)
From: Claude Schochet <claude@math.wayne.edu>
Subject: For the topologist email list (fwd)

This is the second of two questions posted by Claude Schochet for
Chris Phillips.  You may respond to the list or to Claude.

        Let X be locally compact sigma-compact and have finite covering
dimension. Let E be a locally trivial fiber bundle over X, with fiber F
and compact structure group G. I want to extend E to a locally trivial
fiber bundle over some compactification of X; it is equivalent to
consider only the Stone-Cech compactification. Are there known theorems
stating that this can always be done? Suppose I assume in addition that
X is second countable?
        In the case I am interested in, F is the space M_n of n x n
complex matrices, and G is the projective unitary group (U (n) modulo
its center) acting by conjugation. I think I can actually prove what I
need (details not yet checked) by a process of reduction to the case of
complex vector bundles, but it would save some writing if I can find a
theorem to quote. Even a theorem just applying to complex vector bundles
would be helpful.

                                                ---Chris Phillips