Nearness Cosets of the Nearness Groups

Mehmet Ali Öztürk ()
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Mehmet Ali Öztürk: Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, Adıyaman 02040, Turkey

New Mathematics and Natural Computation (NMNC), 2024, vol. 20, issue 03, 935-944

Abstract: In 2019, Öztürk et al. [Gamma semigroups on weak nearness approximation spaces, Journal of the International Mathematical Virtual Institute 9 (2019) 53–72] defined the first algebraic structure on weak nearness approximation spaces which is the gamma semigroup. After this study, the view on the nearness of algebraic structures has completely changed. This view was first expressed in a previous study in 2021 [M. A. Öztürk, Nearness d-algebras, Journal of Algebraic Hyperstructures and Logical Algebras 2 (2021) 73–84]. Our aim is to give the concept of modulo in the nearness group G as in the nearness group (Z, +), where Z is the set of integers. Afterward, based on the concept of modulo in the nearness group G, the nearness cosets of the nearness group G are constructed and its basic properties are examined. Lastly, it is seen that Lagrange theorem is not valid for the nearness subgroups as compared to the usual subgroups.

Keywords: Near sets; nearness approximation spaces; weak nearness approximation spaces; groups; nearness groups; nearness subgroups (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S1793005725500383

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