In this paper we introduce a new type of functions called the generalized regular
continuous functions .These functions are weaker than regular continuous functions and
stronger than regular generalized continuous functions. Also, we study some
characterizations and basic properties of generalized regular continuous functions .Moreover
we study another types of generalized regular continuous functions and study the relation
among them

  In this paper, we introduce a new class of sets, namely , s*g--open sets and we show that the family of all s*g--open subsets of a topological space ) ,X(  from a topology on X which is finer than  . Also , we study the characterizations and basic properties of s*g-open sets and s*g--closed sets . Moreover, we use these sets to define and study a new class of functions, namely , s*g-  -continuous functions and s*g-  -irresolute functions in topological spaces . Some properties of these functions have been studied .

In this paper, we offer and study a novel type generalized soft-open sets in topological spaces, named soft Æ„c-open sets. Relationships of this set with other types of generalized soft-open sets are discussed, definitions of soft Æ„ , soft bc- closure and soft bc- interior are introduced, and its properties are investigated. Also, we introduce and explore several characterizations and properties of this type of sets.

     This paper introduces cutpoints and separations in -connected topological spaces, which are constructed by using the union of vertices set and edges set for a connected graph, and studies the relationships between them. Furthermore, it generalizes some new concepts.

 We use the idea of Grill, this study generalized a new sort of linked space like –connected –hyperconnected and investigated its features, as well as the relationship between it and previously described notation. It also developed new sorts of functions, such as hyperconnected space, and identifying their relationship, by offering numerous instance and attributes that belong to this set. This set will serve as a starting point for further research into the sets many future possibilities. Also, we use some of the theorems and observations previously studied and relate them to the grill and the Alpha group, and benefit from them in order to obtain new results in this research. We applied the concept of Connected to them and obtained

    In this paper, new concepts of maximal and minimal regular s are introduced and discussed. Some basic properties are obtained. The relation between maximal and minimal regular s and some other types of open sets such as regular open sets and   -open sets are investigated.

The topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate

      This paper intends to initiate a new type of generalized closed set in topological space with the theoretical application of generalized topological space. This newly defined set is a weaker form than the -closed set as well as -closed set. Some phenomenal characterizations and results of newly defined sets are inculcated in a proper manner. The characteristics of normal spaces and regular spaces are achieved in the light of the generalized pre-regular closed set.

The goal of this article is to construct fibrewise w-compact (resp. locally w-compact) spaces. Some related results and properties of these concepts will be investigated. Furthermore, we investigate various relationships between these concepts and three classes of fibrewise w-separation axioms.

In this article an attempt has been made to procure the concept of pairwise neutrosophic simply open set, pairwise neutrosophic simply continuous mapping, pairwise neutrosophic simply open mapping, pairwise neutrosophic simply compactness, pairwise neutrosophic simply b-open set, pairwise neutrosophic simply b-continuous mapping, pairwise neutrosophic simply b-open mapping and pairwise neutrosophic simply b-compactness via neutrosophic bi-topological spaces (in short NBTS). Besides, we furnish few illustrative examples on them via NBTS. Further, we investigate some basic properties of them, and formulate several results on NBTSs.