$\mathcal F$-hypercyclic and disjoint $\mathcal F$-hypercyclic properties of binary relations over topological spaces

Abstract

We examine various types of $\mathcal F$-hypercyclic ($\mathcal F$-topologically transitive) and disjoint $\mathcal F$-hypercyclic (disjoint $\mathcal F$-topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.

Keywords

• ${\mathcal f}$-hypercyclic binary relation
• ${\mathcal f}$-topologically transitive binary relation
• disjoint ${\mathcal f}$-hypercyclic binary relation
• disjoint ${\mathcal f}$-topologically transitive binary relation
• digraph