Compact-Open and Point Wise Convergence Topologies - Open Access Library Journal

OALibJ > Vol.5 No.8, August 2018

Compact-Open and Point Wise Convergence Topologies ()

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DOI: 10.4236/oalib.1104775 883 Downloads 2,100 Views

Author(s)

Mohammed Nokhas Murad Kaki

Affiliation(s)

Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, Iraq.

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.

KEYWORDS

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

Share and Cite:

Kaki, M. (2018) Compact-Open and Point Wise Convergence Topologies. Open Access Library Journal, 5, 1-5. doi: 10.4236/oalib.1104775.

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