The present study concentrates on the new generalizations of the Jordan curve theorem. In order to achieve our goal, new spaces namely PC-space and strong PC-space are defined and studied their properties. One of the main concepts that use to define the related classes of spaces is paracompact space. In addition, the property of being PC-space and strong PC-space is preserved by defining a new type of function so called para-perfect function.
Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.
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 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
... Show MoreAbstract. In this study, we shall research the fibrewise micro ideal topological spaces over Ḃ, as well as the relationship between fibrewise micro ideal topological spaces over Ḃ and fibrewise micro topological spaces over Ḃ. At first present introduces a novel notion from fibrewise micro ideal topological spaces over Ḃ, and differentiates it from fibrewise micro topological spaces over Ḃ. Some fundamental characteristics from these spaces are studied. Then show discussed the fibrewise micro ideal closed and micro ideal open topologies. Many propositions relating to these ideas are offered. In the next part will study defines and investigates novel conceptions from fibrewise micro ideal topological spaces over Ḃ, particularly f
... Show MoreIn 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 t
... Show MoreThe theory of Topological Space Fiber is a new and essential branch of mathematics, less than three decades old, which is created in forced topologies. It was a very useful tool and played a central role in the theory of symmetry. Furthermore, interdependence is one of the main things considered in topology fiber theory. In this regard, we present the concept of topological spaces α associated with them and study the most important results.
The main purpose of this paper is to introduce a some concepts in fibrewise bitopological spaces which are called fibrewise , fibrewise -closed, fibrewise −compact, fibrewise -perfect, fibrewise weakly -closed, fibrewise almost -perfect, fibrewise ∗-bitopological space respectively. In addition the concepts as - contact point, ij-adherent point, filter, filter base, ij-converges to a subset, ij-directed toward a set, -continuous, -closed functions, -rigid set, -continuous functions, weakly ijclosed, ij-H-set, almost ij-perfect, ∗-continuous, pairwise Urysohn space, locally ij-QHC bitopological space are introduced and the main concept in this paper is fibrewise -perfect bitopological spaces. Several theorems and characterizations c
... Show MoreNigella sativa has various pharmacological properties and has been used throughout history for a variety of reasons. However, there is limited data about the effects of N. sativa (NS) on human cancer cells. This study aimed at observing the roles of methanolic extract of N. sativa on apoptosis and autophagy pathway in the Human PC3 (prostate cancer) cell line. The cell viability was checked by MTT assay. Clonogenic assay was performed to demonstrate clonogenicity and Western blot was used to check caspase-3, TIGAR, p53, and LC3 protein expression. The results demonstrated that PC3 cell proliferation was inhibited, caspase-3 and p53 protein expression was induced, and LC3 protein expression was modulated. The clonogenic assay showed that PC3
... Show MoreA space X is named a πp – normal if for each closed set F and each π – closed set F’ in X with F ∩ F’ = ∅, there are p – open sets U and V of X with U ∩ V = ∅ whereas F ⊆ U and F’ ⊆ V. Our work studies and discusses a new kind of normality in generalized topological spaces. We define ϑπp – normal, ϑ–mildly normal, & ϑ–almost normal, ϑp– normal, & ϑ–mildly p–normal, & ϑ–almost p-normal and ϑπ-normal space, and we discuss some of their properties.