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A new approach to soft uniform spaces

The purpose of this paper is to introduce the concept of soft uniform spaces and the relationships between soft uniform spaces and uniform spaces. The notions of soft uniform structure, soft uniform continious function, and operations on soft uniform space are introduced and their basic properties are investigated. | Turk J Math (2016) 40: 1071 – 1084 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics http://journals.tubitak.gov.tr/math/ doi:10.3906/mat-1506-98 Research Article A new approach to soft uniform spaces ∗ ¨ ¨ Taha Yasin OZT URK Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, Turkey Received: 30.06.2015 • Accepted/Published Online: 06.12.2015 • Final Version: 21.10.2016 Abstract: The purpose of this paper is to introduce the concept of soft uniform spaces and the relationships between soft uniform spaces and uniform spaces. The notions of soft uniform structure, soft uniform continious function, and operations on soft uniform space are introduced and their basic properties are investigated. Key words: Soft set, soft point, soft topological space, soft diagonal, soft uniform structure, soft uniform space, soft uniform continious function 1. Introduction Many practical problems in economics, engineering, environment, social science, medical science, etc. cannot be dealt with by classical methods because classical methods have inherent difficulties. The reason for these difficulties may be the inadequacy of the theories of parameterization tools. Molodtsov [18] initiated the concept of soft set theory as a new mathematical tool for dealing with uncertainties. Maji et al. [15,16] studied operations over a soft set. The algebraic structure of set theories dealing with uncertainties is an important problem. Many researchers heve contributed towards the algebraic structure of soft set theory. Akta¸s and C ¸ a˘gman [2] defined soft groups and derived their basic properties. Acar et al. [1] introduced initial concepts of soft rings. Feng et al. [10] defined soft semirings and several related notions to establish a connection between soft sets and semirings. Shabir et al. [21] studied soft ideals over a semigroup. Sun et al. [24] defined soft modules and investigated their basic properties. Gunduz and Bayramov [11,12] introduced fuzzy .