TITLE:
Compact-Open and Point Wise Convergence Topologies
AUTHORS:
Mohammed Nokhas Murad Kaki
KEYWORDS:
Compact-Open Topology, Transitive Set, Chaotic Sets, Point Wise Convergence Mixing
JOURNAL NAME:
Open Access Library Journal,
Vol.5 No.8,
August
14,
2018
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.