From a theorem of Van Nall it is known that inverse limits with sequences of upper semi-continuous set-valued functions with 0-dimensional values have dimension bounded by the dimensions of the factor spaces. Information is also available about the dimension of inverse limits with sequences of upper semi-continuous continuum-valued bonding functions having graphs that are mappings on the factor...

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

We prove that the subdifferential of any semi-algebraic extended-real-valued function on Rn has n-dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.

We present a theorem of Sard type for semi-algebraic set-valued mappings whose graphs have dimension no larger than that of their range space: the inverse of such a mapping admits a single-valued analytic localization around any pair in the graph, for a generic value parameter. This simple result yields a transparent and unified treatment of generic properties of semi-algebraic optimization pro...