COMPACT COMPLEMENT TOPOLOGIES IN BITOPOLOGICAL SPACE

Let $(X, \tau_{0}, \tau_{1})$ be a Hausdorff space, where $X$ is an infinite set. The compact complement topologies in bitopological space $(X, \tau_{0}, \tau_{1})$ are $\tau_{0}^*$ and $\tau_{1}^*$ where $\tau_{0}^*$ = $\{\emptyset\}$ $\cup$ $\{X \setminus M_{0} : M_{0}$ is $\tau_{0}$-compact\} and $\tau_{1}^*$ = $\{\emptyset\}$ $\cup$ $\{X \setminus M_{1} : M_{1}$ is $\tau_{1}$-compact\}. Throughout this paper, some properties of the space $(X, \tau_{0}^*, \tau_{1}^*)$ are studied in $ZF$ and we prove some conditions hold in $ZF$.

Introduction to Neutrosophic Soft Bitopological Spaces

In this study, the concept of neutrosophic soft bitopological space is defined and it is one of the few studies that have dealt with this concept. In addition, pairwise neutrosophic soft open (closed) set on neutrosophic soft bitopological spaces are studied. Supra neutrosophic soft topology is defined by pairwise neutrosophic soft open sets. Important theorems related to the subject supported with many examples for a better understanding of the subject are given.

Continuity and Compactness on Neutrosophic Soft Bitopological Spaces

In this manuscript, continuity, compactness and concepts in neutrosophic soft bitopological space have been defined using star bineutrosophic soft open notion. Theorems and properties concerning to these two notions have been investigated here.

Neutrosophic Soft Tri-Topological Spaces

In this study, the concept of neutrosophic soft tri-topological space is defined as a generalization of neutrosophic soft bitopological space. Then neutrosophic soft tri-open and tri-closed sets are defined and in this space. Also, some basic properties of these new types of open and closed sets are investigated and supported by many examples to further clarify the study.

Neutrosophic Soft Bitopological Spaces

In this paper, we built bitopological space on the concept of neutrosophic soft set, we defined the basic topological concepts of this spaces which are N3-(bi)*-open set, N3-(bi)*-closed set, (bi)*-neutrosophic soft interior, (bi)* neutrosophic soft closure, (bi)*-neutrosophic soft boundary, (bi)*-neutrosophic soft exterior and we introduced their properties. In addition, we investigated the relations of these basic topological concepts with their counterparts in neutrosophic soft topological spaces and we introduced many examples.

On Generalized β-Open Sets in Ideal Bitopological Space

In this article, we introduce and study the concepts of γij -semi-I-open sets and γij -βI-open sets by generalizing (i, j)-semi-I-open sets and (ij)-βI-open sets, respectively, in ideal bitopological spaces with an operation γ : τ → P(X). Further, we describe and study (γ, δ)ij -semi-I-continuous and (γ, δ)ij -βI-continuous functions in ideal bitopological spaces and their related notions. In addition, various examples and counterexamples are given for answers to some questions raised in this study.