From: "Claude Schochet" <claude@math.wayne.edu>
Date: Fri, 16 Feb 2007 08:47:19 -0500

If X is compact
then you can write it as an inverse limit of finite complexes X_j (take
nerves of finite covers). Suppose that E \to X is a fibre bundle over X.
Then can you write the bundle as the inverse limit of bundles over X_j ?
This does work for vector bundles at the level of K-theory, since 

K0(X) = dirlim K0(X_j)

But I need it actually at the level of bundles. Also, the fibre would have
to be fixed throughout. 

CS