Graph-approximation of multivalued weighted maps

Abstract

In this paper we study the existence of weighted graph-approximations of $w$-carriers whose values satisfy a certain $w$-$UV$-property. In particular, we prove that any upper semicontinuous set-valued map with compact and acyclic values (with respect to the Čech homology with rational coefficients) from a compact ANR to an ANR admits arbitrarily close weighted graph-approximations.