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https://ptsldigital.ukm.my/jspui/handle/123456789/500586| Title: | Bipolar soft topological spaces and the dynamical systems of bipolar soft topological spaces and dendrites |
| Authors: | Fadel Asmaa Belal Mohammad (P93153) |
| Supervisor: | Syahida Che Dzul-Kifli, Dr. |
| Keywords: | Bipolar soft topological Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia |
| Issue Date: | 11-Nov-2020 |
| Description: | We begin our work by introducing the notion of bipolar soft topological space on a bipolar soft set along with some definitions and results relevant to it. Then, we investigate the concepts of bipolar soft interior, bipolar soft closure, bipolar soft exterior, bipolar soft boundary and the derived set of a bipolar soft set along with a discussion on their properties and the relations among them. In addition, the notions of bipolar soft separation axioms are investigated. Furthermore, we introduce the definitions of bipolar soft function and the inverse image of bipolar soft set along with basic properties pertaining to them. The concepts of bipolar soft continuous function, bipolar soft open function, bipolar soft closed function, bipolar soft homeomorphism, bipolar soft composite function and bipolar soft inverse function are demonstrated associated with some results related to them. Later, we define the bipolar soft dynamical system along with some bipolar soft dynamical notions. We also propose the notions of five bipolar soft chaos notions, i.e bipolar soft transitive, bipolar soft weakly blending, bipolar soft strongly blending, bipolar soft mixing and bipolar soft locally everywhere onto. The relations between these bipolar soft chaos notions are discussed and some examples are provided to illustrate our work. After defining bipolar soft semi-conjugacy and bipolar soft conjugacywe study which bipolar soft chaos notion is preserved under them. Finally, we discuss some chaotic relations on dendrites. Since, transitivity is a key element in a chaotic dynamical system, we investigate some relations between transitivity, stronger and alternative notions of it on dendrites. Some of our results are extended to compact spaces. The relation between Auslander and Yorke chaos, Devaney chaos and strong dense periodicity on dendrites is also investigated.,Ph.D |
| Pages: | 162 |
| Publisher: | UKM, Bangi |
| Appears in Collections: | Faculty of Science and Technology / Fakulti Sains dan Teknologi |
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| ukmvital_128509+SOURCE1+SOURCE1.0.PDF Restricted Access | 1.46 MB | Adobe PDF |  View/Open |
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