Pure and Applied Mathematics Journal
Volume 3, Issue 6-1, December 2014, Pages: 1-6
Received: Jul. 7, 2014;
Accepted: Aug. 21, 2014;
Published: Sep. 2, 2014
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Mohammed N. Murad Kaki, Math Dept., School of Science, University of Sulaimani, Sulaimani, Iraq
In this paper, we will define a new class of chaotic maps on locally compact Hausdorff spaces called α-type chaotic maps defined by α-type transitive maps. This new definition coincides with Devaney's definition for chaos when the topological space happens to be a metric space. Furthermore, we will study new types of non-wandering points called α-type nonwandering points. We have shown that the α-type nonwandering points imply nonwandering points but not conversely. Finally, we have defined new concepts of chaotic on topological space. Relationships with some other type of chaotic maps are given.
Mohammed N. Murad Kaki,
New Types of Chaos and Non-Wandering Points in Topological Spaces, Pure and Applied Mathematics Journal. Special Issue: Mathematical Theory and Modeling.
Vol. 3, No. 6-1,
2014, pp. 1-6.
Mohammed N. Murad Kaki, Topologically α - Transitive Maps and Minimal Systems Gen. Math. Notes, ISSN 2219-7184; Copyright © ICSRS Vol. 10, No. 2, (2012) pp. 43-53
Mohammed N. Murad Kaki. Topologically α- Type Maps and Minimal α-Open Sets Canadian Journal on Computing in Mathematics, Natural Sciences, Engineering and Medicine Vol. 4 No. 2, (2013)
N. Bourbaki, General Topology Part 1, Addison Wesley, Reading, Mass. 1966.
M. Ganster and I.L. Reilly, Locally closed sets and LC-continuous functions, Internet. J. Math. Math. Sci. 12 (3) (1989), 417–424.
Levine N., Semi open sets and semi continuity in topological spaces. Amer. Math. Monthly. 70(1963). 36-41.
Bhattacharya P., and Lahiri K.B., Semi-generalized closed sets in topology. Indian J. Math. 29 (1987). 376-382.
Levine N., Generalized closed sets in topology, Rend. Cire. Math. Paler no. (2) 19 (1970). 89-96.
Ogata N., On some classes of nearly open sets, Pacific J. Math. 15(1965). 961-970.
Andrijevie D., Some properties of the topology of α-sets, Math. Vesnik, (1994). 1 -10
Mohammed N. Murad Kaki, New types of chaotic maps on topological spaces, International J. of Electrical and Electronic Science(AASCIT), Published online March 20, 2014, 1(1): 1-5
F. Nakaoka and N. Oda: Some applications of minimal open sets, Internet Jr. Math. Math. Sci., 27(2001), no. 8 , 471-476.
Kasahara S., Operation-compact spaces. Mathematica Japonica. 24 (1979).97-105.
Rosas E., Vielina J., Operator- compact and Operator-connected spaces. Scientific Mathematica 1(2)(1998). 203-208.
Maheshwari N. S., and Thakur S. S., On α-irresolute mappings, Tamkang J. Math. 11 (1980). 209- 214.