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Compact-Open and Point Wise Convergence TopologiesDOI: 10.4236/oalib.1104775, PP. 1-5 Subject Areas: Mathematical Analysis Keywords: Compact-Open Topology, Transitive Set, Chaotic Sets, Point Wise Convergence Mixing Abstract
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.
Kaki, M. N. M. (2018). Compact-Open and Point Wise Convergence Topologies. Open Access Library Journal, 5, e4775. doi: http://dx.doi.org/10.4236/oalib.1104775. References
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