Preopen Sets Research Articles

Estimating Pairwise Fuzzy Spaces using Residual Sets Spaces

The main focus of this paper is to introduce the new types of pairwise fuzzy Volterra spaces such as by introducing pairwise fuzzy residual sets in the place of pairwise fuzzy Gδ-sets in the definition of pairwise fuzzy Volterra space, a new kind of fuzzy bitopological space namely, pairwise fuzzy εr-Volterra spaces has been introduced and studied and also by introducing pairwise fuzzy pre-open sets in the place of pairwise fuzzy dense sets in the definition of pairwise fuzzy Volterra space, another kind of fuzzy bitopological space namely, pairwise fuzzy εr-Volterra spaces has been introduced and studied. Some of their characterizations and relationships with the other fuzzy bitopological spaces have been investigated and studied.

Some pairwise weakly fuzzy mappings

The aim of this paper is to introduce some pairwise weakly fuzzy mappings, called pairwise weakly fuzzy δ-semi-pre-continuous mappings and pairwise weakly fuzzy δ-semi pre-open mappings in fuzzy bitopological spaces. The concept of pairwise weakly fuzzy δ-semi-precontinuous mappings is to be introduced in fuzzy bitopological spaces with the help of the concept of (i, j)-fuzzy pre-open and (i, j)-fuzzy δ-semi pre-open set. Then some of its basic properties and characterization theorems are to be investigated. Also the notion of pairwise weakly fuzzy δ-semi-pre-open mappings is to be introduced in fuzzy bitopological spaces with the help of the concept of (i, j)-fuzzy open set and (i, j)-fuzzy δ-semi pre-interior. Some of its basic properties and its relationship with other known mappings are also to be studied.

Some Types of Soft Ordered Maps via Soft Pre open Sets

Some Types of Soft Ordered Maps via Soft Pre open Sets

Pre-irresolute Functions in Closure Spaces

The preopen sets are used to define pre-open functions, preclosed functions, pre-continuous functions, contra-pre-continuous functions and pre-irresolute functions which are investigated. They are also used to introduce a new type of connectedness and compactness in closure spaces, they called p-connectedness and p-compactness respectively.

On Generalized Pre-Continuous Fuzzy Proper Function from a Fuzzy Topological Space to Another Fuzzy Topological Space

The purpose of this paper is to introduce and study the concepts of fuzzy generalized pre-open sets, fuzzy generalized pre-closed sets and generalized pre-continuous fuzzy proper functions. Some of its properties have also been investigated. Relation between continuous fuzzy proper functions and generalized pre-continuous fuzzy proper functions has also been established.

On generalized preopen sets

On generalized preopen sets

On generalized preopen sets

On generalized preopen sets

انواع جديدة من المجاميع المفتوحة

قدمنا في هذا البحث انواع جديدة من المجاميع المفتوحة والتي اطلقنا عليها اسم المجموعة المفتوحة p* والمجموعة شبه المفتوحة p* وقد حصلنا على النتائج التالية: كل مجموعة مفتوحة هي مجموعة مفتوحة p* ومجموعة شبه مفتوحة p* .واعطيت امثلة توضح بان الاتجاه المعاكس قد يكون غير صحيح. المجموعة المفتوحةpre و المجموعة المفتوحة p* هي مجاميع متكافئة. كل مجموعة شبه المفتوحة p* هي مجموعة شبه المفتوحة p .

A covering property with respect to generalized preopen sets

In this paper, we introduce and study the notion of $\mu$-precompact spaces on the observation that each $\mu$-preopen set of a generalized topological space is contained in a $\mu$-open set. The $\mu$-precompactness is weaker than $\mu$-compactness but stronger than weakly $\mu$-compactness of generalized topological spaces.

On B-Open Sets

The aim of this paper is to introduce and study $\mathcal{B}$-open sets and related properties. Also, we define a bi-operator topological space $(X, \tau, T_1, T_2)$, involving the two operators $T_1$ and $T_2$, which are used to define $\mathcal{B}$-open sets. A $\mathcal{B}$-open set is, roughly speaking, a generalization of a $b$-open set, which is, in turn, a generalization of a pre-open set and a semi-open set. We introduce a number of concepts based on $\mathcal{B}$-open sets.

Neutrosophic Pre-open Set in Simple Extended Neutrosophic Topology

Neutrosophic Pre-open Set in Simple Extended Neutrosophic Topology

On soft compact and soft Lindel\"{o}f spaces via soft pre-open sets

On soft compact and soft Lindel\"{o}f spaces via soft pre-open sets

On a topology between Tα and Tγα

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

Characterization of Recent Concepts in Soft Bitopological Space

This paper aims at introducing a soft topology via soft preopen sets. We define soft preopen sets, soft preclosed sets, and prove some of its properties.

On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces

In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic p T 1 2 space and neutrosophic g p T 1 2 space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples.

Pre-\((\omega)\)separation axioms

In this paper we use the notion of \((\omega)\) preopen sets to introduce and study pre-separation axioms in an\((\omega)\)topological space.

Study on frontier, border and exterior sets in inuitionistic topological spaces

Using the idea of intuitionistic preopen set, the concepts of intuitionistic preinterior and intuitionistic preclosure in intuitionistic topology have been studied and several of their properties are proved. Moreover, the attributes of intuitionistic pre border, intuitionistic pre frontier and pre exterior have been presented and studied. Also introduced the properties of intuitionistic alpha frontier, alpha border and alpha exterior have been studied. Many counter examples have been pointed out for the applicable classifications.

Decomposition of supra soft locally closed sets and supra SLC-continuity

In this paper, we introduce two different notions of generalized supra soft sets namely supra A--soft sets and supra soft locally closed sets in supra soft topological spaces, which are weak forms of supra open soft sets and discuss their relationships with each other and other supra open soft sets [{it International Journal of Mathematical Trends and Technology} (IJMTT), (2014) Vol. 9 (1):37--56] like supra semi open soft sets, supra pre open soft sets, supra $alpha$--open sets and supra $beta$--open sets. Furthermore, the soft union and intersection of two supra soft locally closed sets have been obtained. We also introduce two different notions of generalized supra soft continuity namely supra soft A--continuous functions and supra SLC--continuous functions. Finally, we obtain decompositions of supra soft continuity: $f_{pu}$ is a supra soft A--continuous if it is both supra soft semi-continuous and supra SLC--continuous, and also $f_{pu}$ is a supra soft continuous if and only if it is both supra soft pre--continuous and supra SLC--continuous. Several examples are provided to illustrate the behavior of these new classes of supra soft sets and supra soft functions.

GENERALIZED TOPOLOGICAL APPROXIMATION SPACES AND THEIR MEDICAL APPLICATIONS

We generalize Pawlak's approximation space to topological approximation spaces using some topological near opensets, such as regular open sets, semi-open sets, pre-open sets,  -open sets,  -open sets and  -open sets and others. Theproperties of the topological approximations space will be studied. Finally, We applied our results on medical data.

On Pre Rg-Continuous Functions in Topology

In this paper we define and study the concept of pre-Rg-continuous functionsusing preopen sets due to Mashhour et.al (1982) and rg-open sets due to N . Palaniappan(1993). Also,we study the pre-g-regular spaces. Mathematics Subject Classification(2010) : 54A05, 54B05,54C08, 54D10.