ON TOPOLOGICALLY ζ-TRANSITIVE MAPS
Keywords:
ζ-open set, ζ-dense, topologically ζ-transitive, ζ-irresolute map, ζ-transitive point
Abstract
In this paper, we describe and investigate some of properties of a new type of topologically transitive maps called topologically -transitive in a topological space via the concept of -open sets. Some properties of these maps are given and relation among topological transitivity, topological -transitivity and topological -transitivity are discussed
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References
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Department of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq
L. C. Block and W. A. Coppel, Dynamics in One Dimension, Springer Verlag Berlin, (1992).
Ethan Akin, Joseph Auslander and Anima Nagar, Variations on the Concept of Topological Transitivity, arXiv:1601.05614v1 (2016), 33 pages.
H. M. Hasan, On some types of continuity, separation axioms and dimension functions, PhD. Thesis, Duhok University, Duhok, Iraq, (2010).
S. G. Hildebrand, Semi-closure, Texas Journal of Science 22 (1971), 99–112.
S. Jafari, Some properties of quasi θ-continuous functions, Far East J. Math. Sci. 6 (1998), 689–696.
S. Kolyada and L. Snoha, Minimal dynamical systems, Scholarpedia 4(11) (2009):5803. http://www.scholarpedia.org/article/Minimal_dynamical_systems.
P. B. Lahiri, Semi-generalized closed sets in topology, Indian J. Math. 29 (1987), 373–382.
N. Levine, Semi-open sets and semi-continuity in topological spaces, American Mathematical Monthly, 70 (1963), 36–41.
S. N. Mahishwari and S. S. Thakur, On α-irresolute mappings, Tamkang J. of Mathematics 11 (1980), 209–214.
M. N. Murad, Topologically α-transitive maps and minimal systems, Gen. Math. Notes 10 (2012), 43–53.
O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961–970.
N. Velicko, H-closed topological spaces, English transl. American Mathematical Society Translations 78 (1968), 103–118.
M. N. Murad, Introduction to θ-transitive maps on topological spaces, International J. of Basic and Applied Sciences (2012), 104–108.
S. N. Maheshwari, V. D. Tapi, Notes on some applications of feebly open sets, Madhya Bharati Jr. Univ. Saugar, (1978–1979).
Z. A. Ameen and B. A. Asaad, A Note on Some Unified Types of Open and Locally Closed Sets, General Letters in Mathematics 4 (2018), 102–106.
Department of Mathematics, College of Science, University of Duhok, Kurdistan Region, Iraq
Published
2023-05-17
How to Cite
KHALAT, D. J., & KHALAF , A. B. (2023). ON TOPOLOGICALLY ζ-TRANSITIVE MAPS. Journal of Duhok University, 26(1), 266-273. https://doi.org/10.26682/sjuod.2023.26.1.26
Section
Pure and Engineering Sciences
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