We define and study new ideas of fibrewise topological space namely fibrewise multi-topological space . We also submit the relevance of fibrewise closed and open topological space . Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space . Furthermore, we propose and prove a number of statements about these ideas. On the other hand, extend separation axioms of ordinary topology into fibrewise setting. The separation axioms are said to be fibrewise multi-T0. spaces, fibrewise multi-T1spaces, fibrewise multi-R0 spaces, fibrewise multi-Hausdorff spaces, fibrewise multi-functionally Hausdorff spaces, fibrewise multi-regular spaces, fibrewise multi-completely regular spaces, fibrewise multi-normal spaces and fibrewise multi-functionally normal spaces. Also we give many score regarding it.. Furthermore, and show the notions of 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. Finally, the concepts are studied fibrewise multi-perfect topological spaces, filter base, contact point, multi-rigid, fibrewise multi-weakly closed, E set, fibrewise almost multi-perfect, multi*-continuous fibrewise multi∗ -topological spaces respectively, multi-Te, locally QHC, In addition, we state and prove several propositions related to these concepts.
The goal of this article is to construct fibrewise w-compact (resp. locally w-compact) spaces. Some related results and properties of these concepts will be investigated. Furthermore, we investigate various relationships between these concepts and three classes of fibrewise w-separation axioms.
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The aim of this paper is to introduce the concept of N and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.
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We examine 10 hypothetical patients suffering from some of the symptoms of COVID 19 (modified) using topological concepts on topological spaces created from equality and similarity interactions and our information system. This is determined by the degree of accuracy obtained by weighing the value of the lower and upper figures. In practice, this approach has become clearer.
Abstract. The minimal or maximal topological space is one of the topological spaces that we will employ in fibrewise locally sliceable and fibrewise locally sectionable. Now in this research I relied on some definitions specific to the research fibrewise maximal and minimal topological spaces. We will define a fibrewise locally minimal sliceable, fibrewise locally maximal sliceable, fibrewise locally minimal sectionable and fibrewise locally maximal sectionable, and I also clarified some examples of them and used them in characteristics by also clarifying them in diagrams.
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In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.
The main purpose of this paper is to introduce a some concepts in fibrewise totally topological space which are called fibrewise totally mapping, fiberwise totally closed mapping, fibrewise weakly totally closed mapping, fibrewise totlally perfect mapping fibrewise almost totally perfect mapping. Also the concepts as totally adherent point, filter, filter base, totally converges to a subset, totally directed toward a set, totally rigid, totally-H-set, totally Urysohn space, locally totally-QHC totally topological space are introduced and the main concept in this paper is fibrewise totally perfect mapping in totally top
The aim of this paper is to look at fibrewise slightly issuances of the more important separation axioms of ordinary topology namely fibrewise said to be fibrewise slightly T0 spaces, fibrewise slightly T1spaces, fibrewise slightly R0 spaces, fibrewise slightly T2 spaces, fibrewise slightly functionally T2 spaces, fibrewise slightly regular spaces, fibrewise slightly completely regular spaces, fibrewise slightly normal spaces. In addition, we announce and confirm many proposals related to these concepts.
The purpose of this paper is to consider fibrewise near versions of the more important separation axioms of ordinary topology namely fibrewise near T0 spaces, fibrewise near T1 spaces, fibrewise near R0 spaces, fibrewise near Hausdorff spaces, fibrewise near functionally Hausdorff spaces, fibrewise near regular spaces, fibrewise near completely regular spaces, fibrewise near normal spaces and fibrewise near functionally normal spaces. Also we give several results concerning it.
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