The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

The main purpose of this paper, is to introduce a topological space , which is induced by reflexive graph and tolerance graph , such that  may be infinite. Furthermore, we offered some properties of  such as connectedness, compactness, Lindelöf and separate properties. We also study the concept of approximation spaces and get the sufficient and necessary condition that topological space is approximation spaces.

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

The impact of mental training overlap on the development of some closed and open skills in five-aside football for middle school students, Ayad Ali Hussein, Haidar Abedalameer Habe

The differential protection of power transformers appears to be more difficult than any type of protection for any other part or element in a power system. Such difficulties arise from the existence of the magnetizing inrush phenomenon. Therefore, it is necessary to recognize between inrush current and the current arise from internal faults. In this paper, two approaches based on wavelet packet transform (WPT) and S-transform (ST) are applied to recognize different types of currents following in the transformer. In WPT approach, the selection of optimal mother wavelet and the optimal number of resolution is carried out using minimum description length (MDL) criteria before taking the decision for the extraction features from the WPT tree

  The purpose of this paper is to study a new types of compactness in bitopological spaces. We shall introduce the concepts of  L- compactness.

      Sequences spaces  , m  ,  p  have called quasi-Sobolev spaces were  introduced   by Jawad . K. Al-Delfi in 2013  [1]. In this  paper , we deal with notion of  quasi-inner product  space  by using concept of  quasi-normed  space which is generalized  to normed space and given a  relationship  between  pre-Hilbert space and a  quasi-inner product space with important  results   and   examples.  Completeness properties in quasi-inner   product space gives  us  concept of  quasi-Hilbert space .  We show  that ,  not  all  quasi-Sobolev spa

This paper is devoted to the discussion the relationships of connectedness between some types of graphs (resp. digraph) and Gm-closure spaces by using graph closure operators.