On bounded and subcontinuous multifunctions
Alois Lechicki · Pacific Journal of Mathematics · 1978
In this paper we extend Kocela's conditions of boundedness of real valued functions to the case of multifunctions.Moreover the concept of subcontinuity (introduced by R. E. Smithson) is considered with application to the following generalization of a result of Ka-Sing Lau:Let F: X -> Y be a point closed and convex multifunction taking values in a locally convex space Y and suppose F is subcontinuous.Then it is /-continuous if and only if for every functional y' EY' the function x -> sup {y '(y ): y G F(x )} is continuous.