F-hypercyclic extensions and disjoint F-hypercyclic extensions of

Abstract

The main aim of this paper is to provide the basic information about F-hypercyclic extensions
of binary relations over topological spaces and disjoint F-hypercyclic extensions of binary relations over
topological spaces. Special attention is paid to the case that the topological space under our consideration
has a linear vector structure, when we also analyze F-hypercyclic multivalued linear extensions of binary
relations and disjoint F-hypercyclic multivalued linear extensions of binary relations. We provide several
illustrative examples and results for simple graphs, digraphs and tournaments.