G-closed Sets Research Articles

A study on J(**) - closed sets in topological spaces

The concept of J(**) - closed sets in initiated here. A few interesting peculiarities of J(**) - closed sets are discussed. Moreover relations of J(**) - closed sets with other existing G-closed sets are analysed. Some important characterizations are also obtained.

Some Properties of α^g-Closed Sets in Fuzzy Neutrosophic Topology

The present paper offers a new notion of sets known as fuzzy neutrosophic ^g-closed sets in fuzzy neutrosophic topology. It is an extended form of work conducted by Fatimah et.al. [1-3]. It investigates several properties of fuzzy neutrisophic ^ g- closed sets and explores a number of examples as to shed the light on the new characteristics of ^g-closed sets as well as some associated relations between them with other sets.

TOPOLOGY BASED ON NEW GENERALIZED CLOSED SETS

In this paper, we introduce a new classes of sets called Ẽ-closed sets and Ẽα-closed sets in topological spaces and we study some of its basic properties. This class lies between the class of closed sets and the class of g-closed sets.

γpg**- Closed Set in Topological Spaces

Abstract 
 In this paper we investigate the definitions of g-closed sets, gp-closed sets, pg-closed sets, gsp-closed sets, g -closed sets, g-closed sets. we introduced a new class of set called γpg**-closed sets which is settled properly in between the class of semi-closed and the class of g**-closed sets .

A new class of NeutroOpen, NeutroClosed, AntiOpen and AntiClosed sets in NeutroTopological and AntiTopological spaces

A lot of research has been done on the types of open and closed sets in general topological spaces and also in general bitopological spaces. Types of sets like pre-open sets and pre-closed sets, semi-open sets and semi-closed sets, Alpha-open sets, and Alpha-closed sets, regular open sets and regular closed sets, g-open sets and g-closed sets, and many more have been defined and studied. In the current study, an attempt has been made to define and give examples of a new category of open and closed sets, namely, NeutroOpen and NeutroClosed sets. Further, the concept of neutron-topology is used to define NeutroPreOpen and NeutroPreClosed sets, NeutroSemiOpen and NeutroSemiClosed sets, NeutroAlphaOpen and NeutroAlphaClosed sets, NeutroRegularOpen and NeutroRegularClosed sets, NeutroBetaOpen, and NeutroBetaClosed sets, and several examples have been given to illustrate each of the new classes of sets. Also, the concept of AntiTopology has been used to define another class of sets, namely, AntiOpen and AntiClosed sets of the above five classes of sets, namely, regular-openclosed; semi-openclosed, Alpha-openclosed, Beta-openclosed pre-openclosed sets. Further, a new class of subsets is identified which are named as NeutroTauOpen and NeutroTauClosed sets. Similar subsets in anti-topological spaces are named as AntiTauOpen and AntiTauClosed sets.

On Neutrosophic Crisp Generalized Alpha Generalized Closed Sets

This study reveals new concepts of neutrosophic crisp closed sets named neutrosophic crisp g-closed sets, neutrosophic crisp αg-closed sets, neutrosophic crisp gα-closed sets, and neutrosophic crisp gαg-closed sets. Furthermore, their ultimate features in neutrosophic crisp topological spaces are examined. Moreover, the consequent new concepts are introduced, such as neutrosophic crisp gαg-closure and neutrosophic crisp gαg-interior and finding some of their characteristics.

Generalizations of regular and normal spaces II

A family m_X of subsets of a nonempty set X is called an m-structure. A set X with a topology_x001C_ and m-structure mX is called a mixed-space and is denoted by (X,tau,m_X). As a generalization of g-closed sets due to Levine, we introduce the notion of mg-closed sets in (X,tau,m_X). By using m_g-open sets, we define and investigate mixed-regularity and mixed-normality in (X,tau,m_X). As special cases, we obtain I_g-regular spaces and s-normal spaces.

ON NANO Ώ-CLOSED SETS

we introduce a new class of sets namely nano y-closed sets in nano topological spaces. This class lies between the class of nano closed sets and the class of nano g-closed sets. This class also lies between the class of nano closed sets and the class of nano -closed sets.

Some new concepts in soft nano topological spaces

The notions of-soft nano subspaces, soft nano-closure and soft nano interior-in soft nano topological spaces are-introduced. Also, a new classes of sets namely weakly-soft nano g-closed sets, weakly soft nano-g-open sets and corresponding-closure and interior are introduced and their properties are investigated.. Further, the inter-relationship between-these new classes of soft nano sets with existing soft nano sets in soft nano topological spaces-are-studied.

G*-closed sets in intuitionistic fuzzy topological spaces

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper we introduce and study the concepts of intuitionistic fuzzy g*-closed sets and intuitionistic fuzzy g*-open sets in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy g*-closed sets lies between intuitionistic fuzzy g-closed sets and intuitionistic fuzzy g-closed sets. We obtained some characterisations and several preservation theorems of the spaces.

Binary Regular ^ Generalized Closed Sets In Binary Topological Spaces

In this article, we introduce binary regular ^ generalized closed sets <strong>(shortly µ<sub>b</sub> r^g-closed sets) </strong>in binary topological spaces. Also we examine some of its properties. Furthermore we study the relationship between these binary r^g-closed sets with other binary closed sets in binary topological spaces.

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Between closed and Ig-closed sets

The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called ρIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ρIg-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that Iclosed and closed-I are independent concepts, as well as I∗-closed sets and closed-I concepts.

G*-CLOSED SETS IN INTUITIONISTIC FUZZY TOPOLOGICAL SPACES

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper we introduce and study the concepts of intuitionistic fuzzy g*-closed sets and intuitionistic fuzzy g*-open sets in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy g*-closed sets lies between intuitionistic fuzzy g-closed sets and intuitionistic fuzzy g-closed sets. We obtained some characterisations and several preservation theorems of the spaces.

From Microstructure-Independent Formulas for Composite Materials to Rank-One Convex, Non-quasiconvex Functions

Examples of non-quasiconvex functions that are rank-one convex are rare. In this paper we construct a family of such functions by means of the algebraic methods of the theory of exact relations for polycrystalline composite materials, developed to identify G-closed sets of positive codimensions. The algebraic methods are used to construct a set of materials of positive codimension that is closed under lamination but is not G-closed. The well-known link between G-closed sets and quasiconvex functions and sets closed under lamination and rank-one convex functions is then used to construct a family of rotationally invariant, nonnegative, and 2-homogeneous rank-one convex functions, that are not quasiconvex.

On s-weakly gw-closed sets in w-spaces

The purpose of this note is to introduce the notion of s-weakly gw-closed set in w-spaces and to study its some basic properties. In particular, the relationships among wg-closed sets, w-semi-closed sets and s-weakly g-closed sets are investigated.

Soft supra strongly generalized closed sets

The notions of supra soft topological space were first introduced by El-Sheikh et al. (5). In this paper, we introduce the concept of soft supra strongly generalized closed sets (soft supra strongly g-closed for short) in a supra soft topological space (X, μ, E) and study their properties in detail, which is a generalization to the notions of soft strongly g-closed sets (15) and supra generalized closed sets (11). Here, we used the concept of supra soft closure, supra soft interior and supra soft open sets to define soft supra strongly generalized closed sets. The relationship between soft supra strongly generalized closed sets and other existing soft sets have been investigated. Furthermore, the union and intersection of two soft supra strongly generalized closed (resp. open) sets have been obtained. It has been pointed out in this paper that many of these parameters studied have, in fact, applications in real world situations and therefore I believe that this is an extra justification for the work conducted in this paper.

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Characterization of Fuzzy δg*-Closed Sets in Fuzzy Topological Spaces

The purpose of this research article is to explain the meaning of g-closed sets in fuzzy topological spaces, which is more understandable to the readers and we find some of its basic properties. The concept of fuzzy sets was introduced by Zadeh in his classical paper (1965). Thereafter many investigations have been carried out, in the general theoretical field and also in different applied areas, based on this concept. The idea of fuzzy topological space was introduced by Chang (1968). The idea is more or less a generalization of ordinary topological spaces. Different aspects of such spaces have been developed, by several investigators. This paper is also devoted to the development of the theory of fuzzy topological spaces.

On a class of sets between μ-closed sets and μg-closed sets

In this paper, a new class of sets called μ*g-closed sets are introduced and investigated with the help of μ-open and μg-open sets. Relationships between this new class and other related classes of sets are established. Some separation axioms has also being studied. Finally, some preservation theorems have been given.