In this paper, we have investigated and introduced some new definitions of\ntransitivity on the set of all continuous maps, denoted by....., called\nthe point-wise convergence transitive, the compact-open transitive and point\nwise convergence topological transitive sets. Relationship between these new\ndefinitions is studied. Finally, we have introduced a number of very important\ntopological concepts and shown that every compact-open convergence\ntransitive map implies point wise transitive maps but the converse not necessarily\ntrue.
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