On almost $ell$-continuous multifunctions

Abstract

The aim of this paper is to introduce a new class of multifunctions between topological spaces, namely almost $ell$-continuous multifunctions, which properly contains the class of $ell$-continuous multifunctions introduced by Sakalova in 1989. We relate this class of multifunctions to other classes of multifunctions, and provide characterizations of related concepts especially in terms of an appropriate change of topology.