Compact-Open and Point Wise Convergence Topologies

摘要

In this paper, we have investigated and introduced some new definitions of transitivity on the set of all continuous maps, denoted by , called the point-wise convergence transitive, the compact-open transitive and point wise convergence topological transitive sets. Relationship between these new defini-tions is studied. Finally, we have introduced a number of very important topo-logical concepts and shown that every compact-open convergence transitive map implies point wise transitive maps but the converse not necessarily true.