  For an upper semi-continuous set-valued mapping from one topological space to
another and for a lower semi-continuous function defined on the product of
these spaces, Berge's theorem states lower semi-continuity of the minimum of
this function taken over the image sets. It assumes that the image sets are
compact. For Hausdorff topological spaces, this paper extends Berge's theorem
to set-valued mappings with possible noncompact image sets and studies relevant
properties of minima.
