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 sectionable totally topological spaces. One the other hand, we studied fibrewise totally forms of the more essential separation axioms of ordinary topology namely fibrewise totally T_0 spaces, fibrewise totally T_1 spaces, fibrewise totally R_0 spaces, fibrewise totally Hausdorff spaces, fibrewise totally functionally Hausdorff spaces, fibrewise totally regular spaces, fibrewise totally completely regular spaces, fibrewise totally normal spaces and fibrewise totally functionally normal spaces. Too we add numerous outcomes about it. As well as, we introduced a notion fibrewise totally compact and fibrewise locally totally compact topological spaces. Finally, we introduced a notion fibrewise totally perfect topological spaces, fibrewise weakly totally closed topological spaces, fibrewise totally rigidlly sets, fibrewise totally almost perfect topological spaces and fibrewise T^*topological spaces. We study several theorm and characterizations converning these concepts.
In this paper, we procure the notions of neutrosophic simply b-open set, neutrosophic simply b-open cover, and neutrosophic simply b-compactness via neutrosophic topological spaces. Then, we establish some remarks, propositions, and theorems on neutrosophic simply
b-compactness. Further, we furnish some counter examples where the result fails.
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This paper intends to initiate a new type of generalized closed set in topological space with the theoretical application of generalized topological space. This newly defined set is a weaker form than the -closed set as well as -closed set. Some phenomenal characterizations and results of newly defined sets are inculcated in a proper manner. The characteristics of normal spaces and regular spaces are achieved in the light of the generalized pre-regular closed set.
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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This paper aims to define and study new separation axioms based on the b-open sets in topological ordered spaces, namely strong - -ordered spaces ( ). These new separation axioms are lying between strong -ordered spaces and - - spaces ( ). The implications of these new separation axioms among themselves and other existing types are studied, giving several examples and counterexamples. Also, several properties of these spaces are investigated; for example, we show that the property of strong - -ordered spaces ( ) is an inherited property under open subspaces.
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In this paper, new concepts of maximal and minimal regular s are introduced and discussed. Some basic properties are obtained. The relation between maximal and minimal regular s and some other types of open sets such as regular open sets and -open sets are investigated.
In this article an attempt has been made to procure the concept of pairwise neutrosophic simply open set, pairwise neutrosophic simply continuous mapping, pairwise neutrosophic simply open mapping, pairwise neutrosophic simply compactness, pairwise neutrosophic simply b-open set, pairwise neutrosophic simply b-continuous mapping, pairwise neutrosophic simply b-open mapping and pairwise neutrosophic simply b-compactness via neutrosophic bi-topological spaces (in short NBTS). Besides, we furnish few illustrative examples on them via NBTS. Further, we investigate some basic properties of them, and formulate several results on NBTSs.
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Our main interest in this study is to look for soft semi separations axioms in soft quad topological spaces. We talk over and focus our attention on soft semi separation axioms in soft quad topological spaces with respect to ordinary points and soft points. Moreover study the inherited characteristics at different angles with respect to ordinary points and soft points. Some of their central properties in soft quad topological spaces are also brought under examination.
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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The aims of this study are to explore the commercial artifacts in the following three kinds of vegetables oils, Nigella Sativa, Trigonella foenum-graecum Linn,and Zingiber officinale. These oils have been very popular medicinal plants which are commonly used in traditional medicine .These commercial oils have been compared with the extracts of these plants.
The physical properties of extracts and commercial oils of these plants have been stuied. We observed that the refractive index of the plants matches and non-significant, while specific gravity of Nigella Sativa has similar specific gravity in both extracts and commercial oil in contrast with Trigonella foenum Linn,and Zingiber officinale and we found significant difference (P<
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.