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 slightly T_2 spaces, fibrewise slightly functionally Hausdorff spaces, fibrewise slightly regular spaces, fibrewise slightly completely regular spaces, fibrewise slightly normal spaces, and fibrewise slightly functionally normal spaces have been extend. In addition, we introduce many propositions related to these concepts. Furthermore, and show the notions of fibrewise slightly compact and connected fibrewise slightly topological spaces. Finally, the concepts are studied slightly convergent, slightly directed toward in fibrewise slightly, as well fibrewise slightly perfect topological spaces, fibrewise slightly weakly closed topological spaces, fibrewise slightly almost perfect topological spaces, and fibrewise slightly* topological spaces. Also, study several theorems and characterizations concerning these concepts.
This paper is concerned with introducing and studying the M-space by using the mixed degree systems which are the core concept in this paper. The necessary and sufficient condition for the equivalence of two reflexive M-spaces is super imposed. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are introduced. From an M-space, a unique supratopological space is introduced. Furthermore, the m-continuous (m-open and m-closed) functions are defined and the fundamental theorem of the m-continuity is provided. Finally, the m-homeomorphism is defined and some of its properties are investigated.
The digital revolution had greatly affected the methods through which we communicate, starting from the basic concepts of the internet technology and the web content in addition to the important issues that concern the culture of the digital media, the internet governance and the variation in the digital age in general and the graphic and internal design in particular.
This research addresses an important topic that goes along with the scientific development in the field of the digital design, especially in the internal and graphic designs. This study consists of two sections: the first includes the problem of the study and the need for it. Starting from the problem of the research, there is no clear perception of the formal characte
This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2 and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j = q , δ, a , pre, b, b.
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The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.
In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact
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