Neutrosophic soft compact spaces
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Neutrosophic soft compact spaces Taha Yasin Ozturk1 · Aysun Benek1 · Alkan Ozkan2 Received: 8 January 2020 / Accepted: 14 August 2020 © African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2020
Abstract In this paper, some cover types are defined on neutrosophic soft sets and the concept of compactness on neutrosophic soft topological spaces is presented using these covers. We also defined the concept of locally compactness on neutrosophic soft topological spaces and some properties are investigated. Keywords Neutrosophic set · Neutrosophic soft set · Neutrosophic soft cover neutrosophic soft compactness · Neutrosophic soft locally compactness Mathematics Subject Classification 54D10 · 54D15 · 54D45 · 54E45
1 Introduction In recent years; new set structures are defined which are different from classical set structure which brings a new approach to many problems that cannot be solved in science, social, engineering, medical and similar sciences. The fuzzy set theory [20], intuitionistic set theory [1], soft set theory [12], rough set theory [15] and neutrosophic set theory [17, 18], which lead these set structures, have caused intense interest in all fields of science. Many different studies are presented in all sub-branches of mathematics belonging to these set structures [6–8, 16, 19]. The fuzzy soft set, intuitionistic fuzzy set, intuitionistic fuzzy soft set, neutrosophic soft set combinations of these defined set structures are presented in many important studies [2–5, 9–11, 13, 14]. The class of compact spaces, which is one of the main subjects of classical mathematics, contains closed, bounded subsets of Euclidean spaces and carries the most important proper-
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Alkan Ozkan [email protected] Taha Yasin Ozturk [email protected] Aysun Benek [email protected]
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Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, Turkey
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Department of Mathematics, Faculty of Arts and Sciences, I˘gdır University, I˘gdır, Turkey
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T. Y. Ozturk et al.
ties of these sets in their structure. Therefore, it is important to study the concept of compact spaces in these new set theories. In this study, the concept of compactness on neutrosophic soft topological spaces is presented. Firstly, various neutrosophic soft cover concepts are defined. Later, using these notions, neutrosophic soft compact space and neutrosophic soft set are defined. We also proved necessary theorems. In addition, neutrosophic soft compactness concept and neutrosophic soft separation axioms have been associated. Finally, neutrosophic soft locally compactness concept is defined and some properties are investigated.
2 Preliminary In this section, the basic definitions and theorems of neutrosophic soft sets are given by using [3, 9, 10, 13, 14] for a better understanding of future sections. Definition 2.1. [9] Let X be an initial universe and E be a set of parameters. Let P(X ) denote the set of all neutrosophic sets of X . A neutrosophic soft set F˜ E over X is a set
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