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Fibrewise Slightly Topological Spaces and Their Generalizations
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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.

Publication Date
Wed Dec 01 2021
Journal Name
University Of Baghdad, College Of Education For Pure Sciences / Ibn Al-haitham, Department Of Mathematics
Some Kinds of Fibrewise Totally Topological Spaces
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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 s

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Publication Date
Fri Jan 01 2016
Journal Name
International Journal Of Advanced Scientific And Technical Research
Topological Generalizations of Rough Concepts
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The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

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Publication Date
Mon Mar 06 2023
Journal Name
Baghdad Science Journal
Quotient on some Generalizations of topological group
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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.

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Publication Date
Sun Jan 01 2012
Journal Name
International Mathematical Forum
Fibrewise Near Separation Axioms
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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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Publication Date
Thu Apr 03 2025
Journal Name
Aip Conference Proceedings
Fibrewise locally minimal and maximal sliceable and fibrewise locally minimal and maximal sectionable topology
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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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Publication Date
Mon Jul 01 2019
Journal Name
Journal Of Physics: Conference Series
Fibrewise Pairwise Soft Separation Axioms
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Abstract<p>The main idea of this research is to study fibrewise pairwise soft forms of the more important separation axioms of ordinary bitopology named fibrewise pairwise soft <italic>T</italic> <sub>0</sub> spaces, fibrewise pairwise soft <italic>T</italic> <sub>1</sub> spaces, fibrewise pairwise soft <italic>R</italic> <sub>0</sub> spaces, fibrewise pairwise soft Hausdorff spaces, fibrewise pairwise soft functionally Hausdorff spaces, fibrewise pairwise soft regular spaces, fibrewise pairwise soft completely regular spaces, fibrewise pairwise soft normal spaces and fibrewise pairw</p> ... Show More
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Publication Date
Sat Jan 01 2022
Journal Name
1st Samarra International Conference For Pure And Applied Sciences (sicps2021): Sicps2021
Feeble Hausdorff spaces in alpha-topological spaces using graph
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Publication Date
Thu Jul 01 2021
Journal Name
Journal Of Physics: Conference Series
Compatibility and Edge Spaces in Alpha - Topological Spaces
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Abstract<p>This research presents the concepts of compatibility and edge spaces in <italic>α</italic>-topological spaces, and introduces the <italic>α</italic>-topology combinatorially induced by the <italic>α</italic>-topology. Furthermore, studies the relationship between the <italic>α</italic>-topology on <italic>V</italic> ∪ <italic>E</italic> and the relative <italic>α</italic>-topology on <italic>V</italic>.</p>
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Publication Date
Mon Dec 01 2014
Journal Name
Ain Shams University
New Studies for Topological Generalizations and Uncertainty in Graph Theory
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Topology and its applications occupy the interest of many researching centers in the advanced world. From this point of view and because the near open sets play a very important role in general topology and they are now the research topics of many topologists worldwide and its sets doesn’t enter in fibrewise topology yet. Therefore, we use some of the near open sets to be model for introduce results and new spaces in fibrewise topological spaces. Also, there is a very important role of closure operators in constructing a topological spaces, so we introduce a new closure operators on the power set of vertices on graphs and conclusion theorems and new spaces from it. Furthermore, we discuss the relationships of connectedness between some ty

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Publication Date
Sat Dec 24 2022
Journal Name
Wasit Journal For Pure Science
β*-Regular supra topological spaces
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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.