Sum of Soft Topological Spaces

Tareq M. Al-shami, Ljubiša D. R. Kočinac and Baravan A. Asaad
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Tareq M. Al-shami: Department of Mathematics, Sana’a University, P.O.Box 1247 Sana’a, Yemen
Ljubiša D. R. Kočinac: Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Baravan A. Asaad: Department of Computer Science, College of Science, Cihan University-Duhok, Duhok 42001, Iraq

Mathematics, 2020, vol. 8, issue 6, 1-12

Abstract: In this paper, we introduce the concept of sum of soft topological spaces using pairwise disjoint soft topological spaces and study its basic properties. Then, we define additive and finitely additive properties which are considered a link between soft topological spaces and their sum. In this regard, we show that the properties of being p-soft T i , soft paracompactness, soft extremally disconnectedness, and soft continuity are additive. We provide some examples to elucidate that soft compactness and soft separability are finitely additive; however, soft hyperconnected, soft indiscrete, and door soft spaces are not finitely additive. In addition, we prove that soft interior, soft closure, soft limit, and soft boundary points are interchangeable between soft topological spaces and their sum. This helps to obtain some results related to some important generalized soft open sets. Finally, we observe under which conditions a soft topological space represents the sum of some soft topological spaces.

Keywords: sum of soft topological spaces; additive property; p-soft Ti; soft compactness; soft paracompactness; soft extremally disconnectedness; soft separable; soft continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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