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On ⱨ - supra open sets in supra topological spaces
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The significance fore supra topological spaces as a subject of study cannot be overstated, as they represent a broader framework than traditional topological spaces. Numerous scholars have proposed extension to supra open sets, including supra semi open sets, supra per open and others. In this research, a notion for ⱨ-supra open created within the generalizations of the supra topology of sets. Our investigation involves harnessing this style of sets to introduce modern notions in these spaces, specifically supra ⱨ - interior, supra ⱨ - closure, supra ⱨ - limit points, supra ⱨ - boundary points and supra ⱨ - exterior of sets. It has been examining the relationship with supra open. The research was also enriched with many of characteristics of each concept. Building upon this set classification, we introduced several kinds of maps like supra ⱨ - continuous, supra ⱨ - open, supra ⱨ - tentative, supra ⱨ -globally and supra ⱨ - homeomorphism. Additionally, we have proven a collection of useful relationships for the aforementioned of functions. Furthermore, the research was enhanced with illustrative and refuting examples.

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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Discrete Mathematical Sciences & Cryptography
On β*-supra topological spaces
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In this paper, a new type of supra closed sets is introduced which we called supra β*-closed sets in a supra topological space. A new set of separation axioms is defined, and its many properties are examined. The relationships between supra β*-Ti –spaces (i = 0, 1, 2)   are studied and shown with instances. Additionally, new varieties of supra β*-continuous maps have been taken into consideration based on the supra β*-open sets theory. 

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Publication Date
Wed Nov 13 2024
Journal Name
Aip Conference Proceedings
On Sδ.derived and Sδ.isolated sets in supra topological spaces
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The topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate

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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.

Publication Date
Wed Jan 01 2025
Journal Name
Journal Of Interdisciplinary Mathematics
Some types of fan sets in supra topology
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This paper work new and unprecedented definitions of sets, which we have named supra fan, supra. delta fan, supra. semi delta fan sets, which are generated by three sets of specific type of supra open sets, it was utilized supra open, supra delta open, supra. semi delta open sets with special conditions. It is highlighted many details of these new types of fan sets, their axis, blades and their annular sets using tables. Attention is given to the interior and the closure of these three types in supra topological spaces. The research was further enriched numerous and diverse examples. Subsequently, the focus shifted to supra. semi delta fan sets to prove lemma and theorem.

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Publication Date
Wed Feb 01 2017
Journal Name
International Journal Of Science And Research (ijsr)
Supra-Approximation Spaces Using Mixed Degree System in Graph Theory
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This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.

Publication Date
Tue Jan 01 2019
Journal Name
Sci.int.(lahore)
FILTER BASES AND SUPRA PERFECT FUNCTIONS
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We introduce some new generalizations of some definitions which are, supra closure converge to a point, supra closure directed toward a set, almost supra converges to a set, almost supra cluster point, a set supra H-closed relative, supra closure continuous functions, supra weakly continuous functions, supra compact functions, supra rigid a set, almost supra closed functions and supra perfect functions. And we state and prove several results concerning it

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Publication Date
Thu Aug 15 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Nano M. and nano IM. sets in nano topological spaces
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studied, and its important properties and relationship with both closed and open Nano sets were investigated. The new Nano sets were linked to the concept of Nano ideal, the development of nano ideal mildly closed set and it has been studied its properties. In addition to the applied aspect of the research, a sample was taken from patients infected with viral hepatitis, and by examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous disease.

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Publication Date
Wed Mar 01 2023
Journal Name
Baghdad Science Journal
A Study on Nψβ and Nβψ - Closed sets in Neutrosophic Topological spaces
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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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Publication Date
Sun Dec 01 2024
Journal Name
Baghdad Science Journal
On pre- Open Regular Spaces
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In 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

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Publication Date
Sat Apr 01 2023
Journal Name
Full Text Book Of Minar Congress8
REGULARITY VIA PRE- GENERALIZED OPEN SETS
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By use the notions pre-g-closedness and pre-g-openness we have generalized a class of separation axioms in topological spaces. In particular, we presented in this paper new types of regulαrities, which we named ρg­regulαrity and Sρg­regulαrity. Many results and properties of both types have been investigated and have illustrated by examples.

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