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. 

Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

In this thesis, we study the topological structure in graph theory and various related results. Chapter one, contains fundamental concept of topology and basic definitions about near open sets and give an account of uncertainty rough sets theories also, we introduce the concepts of graph theory. Chapter two, deals with main concepts concerning topological structures using mixed degree systems in graph theory, which is M-space by using the mixed degree systems. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are defined and studied. In chapter three we study supra-approximation spaces using mixed degree systems and primary object in this chapter are two topological

In this paper we define and study new concepts of functions on fibrewise  topological spaces  over  B namely,  fibrewise  weakly  (resp., closure, strongly) continuoac; funttions which are analogous of weakly

(resp., closure,   strongly)   continuous  functions   and  the  main  result is   : Let  <p       : XY  be a fibrewise  closure  (resp.,  weakly,  closure, strongly,  strongly) continuous function,  where  Y  is fibrewise topological  space  over  B and  X  is  a  fibrewise set  which  has  the

in

In This paper, we introduce the associated graphs of commutative KU-algebra. Firstly, we define the KU-graph which is determined by all the elements of commutative KU-algebra as vertices. Secondly, the graph of equivalence classes of commutative KU-algebra is studied and several examples are presented. Also, by using the definition of graph folding, we prove that the graph of equivalence classes and the graph folding of commutative KU-algebra are the same, where the graph is complete bipartite graph.

Research summary

Praise be to God, and prayers and peace be upon our master Muhammad, his family and companions until the Day of Judgment.

As for after:

It is the right of every nation to take care of its scientific heritage, and to reveal its human civilizational impact, and the Arabs are the richest nations in heritage, as they had in every period of time a sign and pride, the Arabs fulfilled their duty towards humanity, and they carried out a large part of their scientific activity towards humanity.

Therefore, highlighting some of the scientific aspects of the civilized activity of the Arabs, and removing some of the illusions spread by some malicious people, is a human duty before it is a national duty.

The D-enantiomers of amino acids have been thought to have relatively insignificant function in biological processes like, D-amino acids are sometimes found in proteins that are not synthesized by ribosomes. While L-amino acids clearly permanent in nature, D-amino acids have previously inapprehensible regulatory roles in the bacterial kingdom, any diverse of bacterial phyla made from these D-amino acids regulate cell wall remodeling in stationary phase and cause biofilm dispersal in aging bacterial communities. Clarification the mechanism by which D-amino acids given cell wall reorganization and biofilm disassembly will undoubtedly discover new paradigms for understanding how extra cytoplasmic processes are regulated as well as lead to d

In this work we explain and discuss new notion of fibrewise topological spaces, calledfibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.