studied, and its important properties and relationship with both closed and open Nano sets were investigated. The new Nano sets were linked to the concept of Nano ideal, the development of nano ideal mildly closed set and it has been studied its properties. In addition to the applied aspect of the research, a sample was taken from patients infected with viral hepatitis, and by examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous disease.

  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 introduce a new class of sets called -generalized b- closed (briefly gb closed) sets. We study some of its basic properties. This class of sets is strictly placed between the class of gp- closed sets and the class of gsp- closed sets. Further the notion of b- space is introduced and studied.

2000 Mathematics Subject Classification: 54A05

 In this paper, we introduce and study the concept of a new class of generalized closed set which is called generalized b*-closed set in topological spaces ( briefly .g b*-closed) we study also. some of its  basic properties and investigate the relations between the associated topology. 

      In this work, the notion is defined by using    and some properties of this set are studied also,  and   Ù€ set are two concepts that are defined by using ; many examples have been cited to indicate that the reverse of the propositions and remarks is not achieved. In addition, new application example of nano was studied.

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

The aim of this paper is to introduce the concept of N  and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.

In this paper we introduce new class of open sets called weak N-open sets and we study the relation between N-open sets , weak N-open sets and some other open sets. We prove several results about them. 

   The purpose of this paper is to study   new  types of open sets in bitopological spaces.    We shall introduce the concepts of  L- pre-open and L-semi-p-open sets

Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.