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OALib Journal期刊
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Compact-Open and Point Wise Convergence Topologies

DOI: 10.4236/oalib.1104775, PP. 1-5

Subject Areas: Mathematical Analysis

Keywords: Compact-Open Topology, Transitive Set, Chaotic Sets, Point Wise Convergence Mixing

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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.

Cite this paper

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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[2]  Chacon, R.V. (1969) Weakly Mixing Transformations Which Are Not Strongly Mixing. Proceedings of the American Mathematical Society, 22, 559-562.
https://doi.org/10.1090/S0002-9939-1969-0247028-5
[3]  Kaki, M.N.M. (2015) Chaos: Exact, Mixing and Weakly Mixing Maps. Pure and Applied Mathematics Journal, 4, 39-42.
https://doi.org/10.11648/j.pamj.20150402.11
[4]  Kaki, M.N.M. (2013) Introduction to Weakly b-Transitive Maps on Topo-logical Space. Science Research, 1, 59-62.
https://doi.org/10.11648/j.sr.20130104.11

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