Csaszar introduced the concept of generalized topological space and a new open set in a generalized topological space called -preopen in 2002 and 2005, respectively. Definitions of -preinterior and -preclosuer were given. Successively, several studies have appeared to give many generalizations for an open set. The object of our paper is to give a new type of generalization of an open set in a generalized topological space called -semi-p-open set. We present the definition of this set with its equivalent. We give definitions of -semi-p-interior and -semi-p-closure of a set and discuss their properties. Also the properties of -preinterior and -preclosuer are discussed. In addition, we give a new type of continuous function

  Let M be an R-module, where R is commutative ring with unity. In this paper we study the behavior of strongly hollow and quasi hollow submodule in the class of strongly comultiplication modules. Beside this we give the relationships between strongly hollow and quasi hollow submodules with V-coprime, coprime, bi-hollow submodules.

   In this paper, we introduce a new type of functions in bitopological spaces, namely, (1,2)*-proper functions. Also, we study the basic properties and characterizations of these functions . One of the most important of equivalent definitions to the (1,2)*-proper functions is given by using (1,2)*-cluster points of filters . Moreover we define and study (1,2)*-perfect functions and (1,2)*-compact functions in bitopological spaces and we study the relation between (1,2)*-proper functions and each of (1,2)*-closed functions , (1,2)*-perfect functions and (1,2)*-compact functions and we give an example when the converse may not be true .
 

The main idea of this research is to consider fibrewise pairwise versions of the more important separation axioms of ordinary bitopology named fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise -Hausdorff spaces, fibrewise pairwise functionally -Hausdorff spaces, fibrewise pairwise -regular spaces, fibrewise pairwise completely -regular spaces, fibrewise pairwise -normal spaces and fibrewise pairwise functionally -normal spaces. In addition we offer some results concerning it.

The primary objective of this paper is to introduce a new concept of fibrewise topological spaces on D is named fibrewise multi- topological spaces on D. Also, we entroduce the concepts of multi-proper, fibrewise multi-compact, fibrewise locally multi-compact spaces, Moreover, we study relationships between fibrewise multi-compact (resp., locally multi-compac) space and some fibrewise multi-separation axioms.

The aim of this research is to study some types of fibrewise fuzzy topological spaces. The six major goals are explored in this thesis. The very first goal, introduce and study the notions types of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j={δ,θ,α,p,s,b,β} The second goal is to introduce weak and strong forms of fibrewise fuzzy ω-topological spaces, namely the fibrewise fuz

In this work we define and study new concept of fibrewise topological spaces, namely fibrewise soft topological spaces, Also, we introduce the concepts of fibrewise closed soft topological spaces, fibrewise open soft topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces.

      In this paper, we introduced module that satisfying strongly -condition modules and strongly -type modules as generalizations of t-extending. A module  is said strongly -condition if for every submodule of  has a complement which is fully invariant direct summand. A module   is said to be strongly -type modules if every t-closed submodule has a complement which is a fully invariant direct summand. Many characterizations for modules with strongly -condition for strongly -type module are given. Also many connections between these types of module and some related types of modules are investigated.

Die vorliegende Forschung handelt es um die Satzfelder, besonders das Mittelfeld des Satzes im deutschen und Arabischen. Diese Forschung wurde mit der Satzdefinition, Satzglieder begonnen, damit wir diese klar werden und dann werden die Felder des Satzes gut gekannt. Der erste Abschnitt schlieβt auch den Mittelfeld des Satzes und, wie man das Feld erkennen und bestimmen kann. Die Forschung untersucht auch. Ob es in der arabischen Sprache den selben Struktur wie im Deutschen gibt, z.B Bildung des Satzes sowie Satzfelder bezügllich das Mittelfeld.

Der zweite Abschnitt handelt sich um den arabischen Teil und behandelt die Wortarten im Arabischen sowie den Satz als auch Satzarten (Nominal- Verbal- Halbsatz).

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