Various Types of Supra Pre-compact and Supra Pre-Lindelöf Spaces

Al-shami, Tareq M.; Asaad, Baravan A.; El-Gayar, Mostafa A.

doi:10.35834/2020/3201001

Cited by 9 publications

(8 citation statements)

References 19 publications

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“…A pair (A, μ A ) is called a supra subspace of (X, μ). Definition 8 (see [11]). β is called a basis for a supra topology (X, μ) if every member of μ can be expressed as a union of elements of β.…”

Section: Remarkmentioning

confidence: 99%

“…β is called a basis for a supra topology (X, μ) if every member of μ can be expressed as a union of elements of β. Definition 9 (see [11]). Let (X i , μ i ): i � 1, 2, .…”

Section: Remarkmentioning

confidence: 99%

“…ese generalizations have been utilized to define new versions of compactness and connectedness, see, for example [9][10][11][12][13][14]. Mustafa and Qoqazeh [15] took advantage of supra D-sets to define separation axioms on supra topological spaces.…”

Section: Introductionmentioning

confidence: 99%

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Some Applications of Supra Preopen Sets

El-Shafei

Zakari

Al-shami

2020

Journal of Mathematics

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The aim of this work is to define some concepts on supra topological spaces using supra preopen sets and investigate main properties. We started this paper by correcting some results obtained in previous study and presenting further properties of supra preopen sets. Then, we introduce a concept of supra prehomeomorphism maps and discuss its main properties. After that we explore the concepts of supra limit and supra boundary points of a set with respect to supra preopen sets and examine their behaviours on the spaces that possess the difference property. Finally, we formulate the concepts of supra pre-Ti-spaces i=0,1,2,3,4 and give completely descriptions for each one of them. In general, we study their main properties in detail and show the implications of these separation axioms among themselves as well as with STi-space with the help of some interesting examples.

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Section: Remarkmentioning

confidence: 99%

“…β is called a basis for a supra topology (X, μ) if every member of μ can be expressed as a union of elements of β. Definition 9 (see [11]). Let (X i , μ i ): i � 1, 2, .…”

Section: Remarkmentioning

confidence: 99%

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Some Applications of Supra Preopen Sets

El-Shafei

Zakari

Al-shami

2020

Journal of Mathematics

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“…Al-shami [18] investigated the classical topological notions such as limit points of a set, compactness, and separation axioms on the STSs. Investigation of several types of compactness and Lindelöfness was the goal of some papers such as [19][20][21][22]. Al-shami [23] introduced the concept of paracompactness on STSs and explored main properties.…”

Section: Introductionmentioning

confidence: 99%

Applications of some operators on supra topological spaces

Asaad

Al-shami

Abo-Tabl

2020

Demonstratio Mathematica

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In this paper, the notion of an operator \gamma on a supra topological space (X,\mu ) is studied and then utilized to analyze supra \gamma -open sets. The notions of {\mu }_{\gamma }-g.closed sets on the subspace are introduced and investigated. Furthermore, some new {\mu }_{\gamma }-separation axioms are formulated and the relationships between them are shown. Moreover, some characterizations of the new functions via operator \gamma on \mu are presented and investigated. Finally, we give some properties of {S}_{(\gamma ,\beta )}-closed graph and strongly {S}_{(\gamma ,\beta )}-closed graph.

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“…In 2016, Alshami [8] discussed the concepts of compactness and separation axioms on supra topological spaces. en, Al-Shami [9,10] and Al-shami et al [11] presented new types of supra compact spaces using supra α-open, supra semiopen, and supra preopensets. Later, the authors of [12][13][14][15] employed some generalizations of supra opensets to investigate several kinds of supra limit points of a set and supra T i spaces (i � 0, 1, 2, 3, 4).…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Ideal Supra Topological Spaces

Abbas

2020

Advances in Fuzzy Systems

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In this paper, we introduce the notion of fuzzy ideals in fuzzy supra topological spaces. The concept of a fuzzy s-local function is also introduced here by utilizing the s-neighbourhood structure for a fuzzy supra topological space. These concepts are discussed with a view to find new fuzzy supra topologies from the original one. The basic structure, especially a basis for such generated fuzzy supra topologies, and several relations between different fuzzy ideals and fuzzy supra topologies are also studied here. Moreover, we introduce a fuzzy set operator Ψ S and study its properties. Finally, we introduce some sets of fuzzy ideal supra topological spaces (fuzzy ∗ -supra dense-in-itself sets, fuzzy S ∗ -supra closedsets, fuzzy ∗ -supra perfect sets, fuzzy regular-I-supra closedsets, fuzzy-I-supra opensets, fuzzy semi-I-supra opensets, fuzzy pre-I-supra opensets, fuzzy α -I-supra opensets, and fuzzy β -I-supra opensets) and study some characteristics of these sets, and then, we introduce some fuzzy ideal supra continuous functions.

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Various Types of Supra Pre-compact and Supra Pre-Lindelöf Spaces

Cited by 9 publications

References 19 publications

Some Applications of Supra Preopen Sets

Some Applications of Supra Preopen Sets

Applications of some operators on supra topological spaces

Fuzzy Ideal Supra Topological Spaces

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