This paper gives necessary and sufficient conditions for We do so by introducing a class of
transfer continuities which characterize the essence of topological structures of functions
and correspondences for extreme points and significantly weaken the conventional
continuities. Thus our results generalize the classical Weierstrass theorem and the
Maximum Theorem of Berge (Espaces topologiques et fonctions multivoques, Donod, Paris,
1959; Topological Spaces, Macmillan, New York, 1963, p. 116), by giving necessary and …