In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two types of regular spaces have been presented, namely the topological space Rp and the topological space S-Rp. The properties of these two spaces and their relationship with each other, as well as the effect of functions on them, have been studied. In addition several theorems have been proved regarding the sufficient and necessary conditions to make the topological spaces Rp-regular or S-Rp-regular. The above concepts have been linked with a new type of Hausdorff space and the concepts under study are reinforced with examples.
Abstract
The study aims to identify the common fears of preschool children and their relationship to the approaches to parental treatment in South Al Batinah Governorate from their mother’s point of view. Total of (466) mothers were selected as the study sample. The researcher used the scale of common fear and the scale of parental treatment approaches. The results of the study have shown that the most common fear among the study sample was (the fear of darkness) in the first level with a rate of 75.03%, and in the second level came the item (my child is afraid to sleep alone) by 72.74%, in the third level came to the item (fear of seeing insects) with a rate of 67.59%, and the last one was (the fear of rain) w
... Show MoreIn 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
... Show MoreLet A ⊆ V(H) of any graph H, every node w of H be labeled using a set of numbers; , where d(w,v) denotes the distance between node w and the node v in H, known as its open A-distance pattern. A graph H is known as the open distance-pattern uniform (odpu)-graph, if there is a nonempty subset A ⊆V(H) together with is the same for all . Here is known as the open distance pattern uniform (odpu-) labeling of the graph H and A is known as an odpu-set of H. The minimum cardinality of vertices in any odpu-set of H, if it exists, will be known as the odpu-number of the graph H. This article gives a characterization of maximal outerplanar-odpu graphs. Also, it establishes that the possible odpu-number of an odpu-maximal outerplanar graph i
... Show MoreThe 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 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 aim of this thesis is to introduce a new concept of fibrewise topological spaces which is said to be fibrewise slightly topological spaces. We generalize some of the main results that have been reached from fibrewise topology into fibrewise slightly topological space. We introduce the concepts of fibrewise slightly closed, fibrewise slightly open, fibrewise locally sliceable, and fibrewise locally sectionable slightly topological spaces. Also, state and prove several propositions related to these concepts. On the other hand, extend separation axioms of ordinary topology into fibrewise setting. The separation axioms are said to be fibrewise slightly T_0 spaces, fibrewise slightly T_1 spaces, fibrewise slightly R_0 spaces, fibrewise s
... Show MoreFibrewise topological spaces theory is a relatively new branch of mathematics, less than three decades old, arisen from algebraic topology. It is a highly useful tool and played a pivotal role in homotopy theory. Fibrewise topological spaces theory has a broad range of applications in many sorts of mathematical study such as Lie groups, differential geometry and dynamical systems theory. Moreover, one of the main objects, which is considered in fibrewise topological spaces theory is connectedness. In this regard, we of the present study introduce the concept of connected fibrewise topological spaces and study their main results.
The concept of fuzzy orbit open sets under the mapping
The combustion and pyrolysis processes of sewage sludge were studied in the current report. Two kinds of sewage sludge(SS) were used, SS the sewage sludge was not treated, while SS-U90KHz the ultrasonic bath pre-treated sewage sludge with a frequency of 90KHz was not treated. Wastewater treatment plants are the origins of waste sludge. Analyses were performed roughly and finally. Thermogravimetric research analyzed the thermal behaviour of the analysed sewage bucket (TGA). The samples were heated at a constant rate of 25 to 800 Celsius by air (combustion) and nitrogen flow (pyrolysis). For sludges which have been investigated. In the TG/DTG curves, comparable thermal profiles were available. All of the TG/curves DTG’s were divided into th
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Although the rapid development in reverse engineering techniques, 3D laser scanners can be considered the modern technology used to digitize the 3D objects, but some troubles may be associate this process due to the environmental noises and limitation of the used scanners. So, in the present paper a data pre-processing algorithm has been proposed to obtain the necessary geometric features and mathematical representation of scanned object from its point cloud which obtained using 3D laser scanner (Matter and Form) through isolating the noised points. The proposed algorithm based on continuous calculations of chord angle between each adjacent pair of points in point cloud. A MATLAB program has been built t
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