Bi Supra Transitive and Semi Minimal Systems
, PP. 1-7 10.4236/oalib.1104749
Keywords: Bi-Supra Topology, Semi Transitive, Semi Minimal Systems, Bi-Supra Transitive Maps
In the present paper, we define and introduce some
new class of topological transitive maps called topological semi-transitive, bi-supra
transitive maps, semi-minimal systems and study some of its properties. The
main results are the following propositions: Every semi-minimal map is a
minimal map, but the converse is not
necessarily true and every bi-supra transitive map is transitive map.
Cite this paper
Jasim, T. H. and Murad, M. N. (2018). Bi Supra Transitive and Semi Minimal Systems.
Open Access Library Journal, 5, e4749. doi: http://dx.doi.org/10.4236/oalib.1104749.
[ 1] Levin, N. (1963) Semi-Open Sets and Semi-Continuity in Topological Spaces. American Mathematical Monthly, 70, 36-40. https://doi.org/10.1080/00029890.1963.11990039
[ 2] Stone, M. (1937) Applications of the Theory of Boolean Rings to General Topology. Transactions of the American Mathematical Society, 41, 374-381. https://doi.org/10.1090/S0002-9947-1937-1501905-7
[ 3] Mashhour, A.S., Abd El-Monsef, M.E. and El-Deep, S.N. (1982) On Pre-Continuous and Weak Pre-Continuous Mappings. Proceedings of the Mathematical and Physical Society of Egypt, 47-53.
[ 4] Velicko, N.V. (1968) H-Closed Topological Spaces. American Mathematical Society Translations: Series 2, 78, 102-118. https://doi.org/10.1090/trans2/078/05
[ 5] Crossley, S.G. and Hildebrand, S.K. (1972) Semi Topological Properties. Fundamenta Mathematicae, 74, 233-254. https://doi.org/10.4064/fm-74-3-233-254
[ 6] Kaki, M.N.M. (2012) New Types of Transitive Functions and Minimal System. International Journal of Basic and Applied Sci-ence, 12, 53-58.
[ 7] Kaki, M.N.M. (2018) Chaos, Mixing Weakly Mixing and Exactness. OALib Journal, 5, 1-6. http://www.oalib.com/journal
[ 8] Kaki, M.N.M. (2014) New Conceptions of Transitivity and Minimal Mappings. Science Research, 2, 1-6.