Concepts of lower semicontinuity and continuous selections for convex valued multifunctions (Q1185260)

The authors consider eight notions of continuity for multivalued functions, defined on a paracompact space and with values in a normed space, all weaker than lower semi-continuity. They study the relations between them and prove a selection theorem extending the classical Michael selection theorem. The case of almost lower semicontinuous functions and of approximate selections, in the sense of \textit{F. Deutsch} and \textit{P. Kenderov}, [SIAM J. Math. Anal. 14, 185-194 (1983; Zbl 0518.41031)] are included. Evaluations of the Hausdorff distances between the graphs of selections and of the multivalued mappings are given.