On $$\varepsilon $$-soft topological semigroups

Abstract

In this paper, we introduce e-right, e-left, e-semi and ε-soft topological semigroups and examine the way these are related to each other. To do so, we need to define -soft and point open soft topologies, which are defined in the third and fourth sections, respectively. Also, soft separation axioms on these soft topologies will be studied. KeywordsSoft topological semigroup • -Soft topology • Point open soft topology • T -soft space Recently, the theory has been studied and used extensively. For example, the basic aspects of soft set theory were developed in Pie and Miao (2005), Maji et al. (2003) and Chen et al. (2005), algebraic structures of soft sets were studied in Acar et al. (2010), Aktas and Cagman (2007), Jun (2008) and Sun et al. (2008), and applications of soft set theory in game theory and measure theory were given in Molodtsov et al. (2006). The study of soft topological spaces Communicated by A. Di Nola.

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

“…The family of all soft closed sets in (X, τ, A) will be denoted by τ c . Soft topological concepts and their applications are still a hot area of research ( [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). The notion of ω-regular TSs was introduced in [23], then the study of ω-regular TSs continued in [24] in which the authors defined and investigated ω-T 2 TSs.…”

Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces

“…Then, many topological concepts were modified to include soft topology. The concepts of soft topology and their applications is still a hot area of research (see for example [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]).…”

Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

“…For a STS (U, τ, E), the members τ are called soft open sets. Soft topological concepts and their applications are still a hot area of research [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The concept of ω-open sets in TSs is defined in [23] as follows: let (U, ) be a TS and V ⊆ U, then V is ω-open set in (U, ) if for each x ∈ V, there is W ∈ such that x ∈ W and W − V is countable, or equivalently, V is ω-open set in (U, ) if and only if for each x ∈ V, there is W ∈ and a countable set C ⊆ U such that x ∈ W −C ⊆ V. Denote the family of all ω-open sets in the TS (U, ) by ω .…”