We study orbit spaces of generalized gradient vector fields for Morse
functions. Typically, these orbit spaces are non-Hausdorff. Nevertheless, they
are quite structured topologically and are amenable to study. We show that
these orbit spaces are locally contractible. We also show that the quotient map
associated to each such orbit space is a weak homotopy equivalence and has the
path lifting property.Comment: 16 pages, 4 figures; strengthened a main result (Corollary 3.5) and
updated the introduction and the conclusio
