Sum of Soft Topological Spaces

• Main Authors: Tareq M. Al-shami, Ljubiša D. R. Kočinac, Baravan A. Asaad
• Format: Article
• Language: English
• Published: MDPI AG 2020-06-01
• Series: Mathematics
• Subjects: sum of soft topological spaces; additive property; p-soft Ti; soft compactness; soft paracompactness; soft extremally disconnectedness
• Online Access: https://www.mdpi.com/2227-7390/8/6/990

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 <inline-formula> <math display="inline"> <semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics> </math> </inline-formula>, 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.