The convergence approach to exponentiable maps
Abstract: Exponentiable maps in the category Top of topological spaces
are characterized by an easy ultrafilter-interpolation property,
in generalization of a recent result by Pisani for spaces. From
this characterization we deduce that perfect (= proper and
separated) maps are exponentiable, generalizing the classical
result for compact Hausdorff spaces. Furthermore, in
generalization of the Whitehead-Michael characterization of
locally compact Hausdorff spaces, we characterize exponentiable
maps of Top between Hausdorff spaces as restrictions of perfect
maps to open subspaces.
