Abstract. Fibrewise micro-topological spaces be a useful tool in various branches of mathematics. These mathematical objects are constructed by assigning a micro-topology to each fibre from a fibre bundle. The fibrewise micro-topological space is then formed by taking the direct limit of these individual micro-topological spaces. It can be adapted to analyze various mathematical structures, from algebraic geometry to differential equations. In this study, we delve into the generalizations of fibrewise micro-topological spaces and explore the applications of these abstract structures in different branches of mathematics. This study aims to define the fibrewise micro topological space through the generalizations that we use in this paper, whi

Topology and its applications occupy the interest of many researching centers in the advanced world. From this point of view and because the near open sets play a very important role in general topology and they are now the research topics of many topologists worldwide and its sets doesn’t enter in fibrewise topology yet. Therefore, we use some of the near open sets to be model for introduce results and new spaces in fibrewise topological spaces. Also, there is a very important role of closure operators in constructing a topological spaces, so we introduce a new closure operators on the power set of vertices on graphs and conclusion theorems and new spaces from it. Furthermore, we discuss the relationships of connectedness between some ty

   In this paper we prove a theorem about the existence and uniqueness common fixed point for two uncommenting self-mappings which defined on orbitally complete G-metric space. Where we use a general contraction condition.
 

In this paper the concepts of weakly (resp., closure, strongly) Perfect Mappings are defined and the important relationships are studied: (a) Comparison between deferent forms of perfect mappings. (b) Relationship between compositions of deferent forms of perfect mappings. (c) Investigate relationships between deferent forms of perfect mappings and their graphs mappings.

Abstract. In this work, some new concepts were introduced and the relationship between them was studied. These concepts are filter directed-toward, nano-closure-directed-toward and nano-closure-converge to point, and some theories and results about these concepts were presented. A definition almost-nano-converges for set, almost-nano-cluster-point, and definition of quasi-nano-Hausdorff-closed and was also called nano-Hausdorff-closed relative, were also presented several theories related to these definitions were presented and the relationship between them was studied . We also provided other generalizations, including nano closure continuous mappings and it was also called as nano-weaklycontinuous- mappings, as well as providing a definit

the electron correlation effect for inter-shell can be described by evaluating the fermi hole and partial fermi hole for Li atom comparing with Be+ and B+2 ions

This paper consist some new generalizations of some definitions such: j-ω-closure converge to a point,  j-ω-closure directed toward a set, almost  j-ω-converges to a set, almost  j-ω-cluster point, a set  j-ω-H-closed relative, j-ω-closure continuous mappings, j-ω-weakly continuous mappings, j-ω-compact mappings, j-ω-rigid a set, almost j-ω-closed mappings and  j-ω-perfect mappings. Also, we prove several results concerning it, where j ÃŽ{q, δ,a, pre, b, b}.