  We describe a general procedure to construct topological extensions of given
skew product maps with one-dimensional fibres, by blowing up a countable number
of single points to vertical segments. This allows to produce various examples
of unusual dynamics, including almost automorphic minimal sets of almost
periodically forced systems, point-distal but non-distal homeomorpisms of the
torus (as first constructed by Rees) or minimal sets of quasiperiodically
forced interval maps which are not filled-in.
