In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

In this thesis, we introduced some kinds of fibrewise topological spaces by using totally continuous function is called fibrewise totally topological spaces. We generalize some fundamental results from fibrewise topology into fibrewise totally topological spaces. We also introduce the concepts of fibrewise totally separation axioms, fibrewise totally compact and locally totally compact topological spaces. As well as fibrewise totally perfect topological spaces. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise totally topological spaces. We, also introduce the concepts of fibrewise totally closed topological spaces, fibrewise totally open topological spaces, fibrewise locally sliceable and locally s

The aim of this paper is to introduce and study the notion type 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}.

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 introduced some types of fibrewise topological spaces by using a near soft set, various related results also some fibrewise near separation axiom concepts and a fibrewise soft ideal topological spaces. We introduced preliminary concepts of topological spaces, fibrewise topology, soft set theory and soft ideal theory. We explain and discuss new notion of fibrewise topological spaces, namely fibrewise soft near topological spaces, Also, we show the notions of fibrewise soft near closed topological spaces, fibrewise soft near open topological spaces, fibrewise soft near compact spaces and fibrewise locally soft near compact spaces. On the other hand, we studied fibrewise soft near forms of the more essent

Background: Any child with Down's syndrome does not develop in the same manner as normal child. Therefore, the child should not be viewed as being like everyone else. Developmental enamel defects in primary teeth have been found at least twice as frequently in disabled children as in control children. Down's syndrome consumed protein more than the recommended daily allowance compared to other disabled groups. Therefore, the aim of this study was to investigate developmental defects of enamel and their relations to nutrient intake among Down's syndrome children in comparison to normal children. Materials and Methods: A sample consisted of fifty institutionalized Down's syndrome children (study group) and 50 normal children (control group)

The problem of housing in Iraq is a long-rooted and rooted problem, and it needs a great effort to find out its causes and thus give essential points that contribute to alleviating and addressing it, and it is worth noting that research into the housing problem and the housing sector in Iraq is not done in isolation from other sectors and studies. As well as the economic policies pursued and the social and political conditions. It is known that the Iraqi economy is a unilateral (rentier) economy, that is, it depends almost entirely on exporting oil and obtaining revenues, and that the economic decision and economic policies followed in Iraq are greatly affected by several factors, including the economic, social and political fact

Abstract

This research aims to identify the effect of measuring reinforcement (regular - irregular) in gamification upon developing computer skills among secondary education students in the Kingdom of Saudi Arabia. The research experiment was applied on two samples of (68) secondary education students in the Kingdom of Saudi Arabia in the Aurar region. The results revealed there is a significant difference between the experimental group that used (irregular) reinforcement and the control group used (regular) reinforcement in gamification through the post-application of the electronic programming test and through the programming, language skills observing card (Visual Basic Studio).