D. Molodtsov (1999) [1] introduced the concept of a soft set as a new approach for modeling uncertainties. Xiao et al. [7] and Pei and Miao [8] discussed the relationship between soft sets and information systems. They showed that soft sets are a class of special information systems. So it’s important to study the structures of soft sets for information systems. Shabir and Naz(2011) [20], studi...

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

The concept of γ-semi-regular-open sets and γ-sclosed spaces have been introduced and explored in [6]. In this paper, we continue studying the properties and characterizations of γ-semi-regular open sets and γ-s-closed spaces.

In this article we originate a new class of Grill Set, namely GSβ-Open which is parallel to the β Open Set in Topological Space (X, θ, G). addition, entitle GSβ-continuous and GSβ-open functions by applying review some its important properties. Many examples are given explain concept lucidly. The properties GSβ open sets investigated studied. theorems based on arbitrary union finite intersectio...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

The aim of this paper is to introduce various functions associated with semi*α-open sets. Here semi*αcontinuous, semi*α-irresolute, contra-semi*α-continuous and contra-semi*α-irresolute functions are defined. Characterizations for these functions are given. Further their fundamental properties are investigated. Many other functions associated with semi*α-open sets and their contra versions are ...

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

In this paper, we extend the notions of γ-operation introduced in [12], by using the soft ideal notions. We introduce the notions of Ĩ-open soft sets, pre-Ĩopen soft sets, α-Ĩ-open soft sets, semi-Ĩ-open soft sets and β-Ĩ-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces with soft ideal. We also introduce the co...