Supra b-compact and supra b-Lindelof spaces

2020

Journal of Mathematics

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.

Section: Introductionmentioning

confidence: 99%

Some Applications of Supra Preopen Sets

El-Shafei

Zakari

2020

Journal of Mathematics

“…In other words, their definitions were formulated using supra interior and supra closure operators instead of interior and closure operators. These generalizations have been utilized to define new versions of compactness, connectedness and separation axioms, see, for example [5,6,17,22,25]. The class of supra R-open sets has been studied in [4,11] under the name of somewhere dense sets.…”

Section: Introductionmentioning

confidence: 99%

Limit Points and Separation Axioms with Respect to Supra Semi-open Sets

Eur. J. Pure Appl. Math.

Abo-Tabl

Assad

et al. 2020

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between certain topological concepts, or preserving some properties under fewer conditions of those on topology. To contribute this research area, in this paper, we establish some new concepts on supra topological spaces using supra semi-open sets and give some characterizations of them. First, we introduce a concept of supra semi limit points of a set and study main properties, in particular, on the spaces that possess the difference property. Second, we define and investigate new separation axioms, namely supra semi Ti-spaces (i = 0, 1, 2, 3, 4) and give complete descriptions for each one of them. We provide some examples to show the relationships between them as well as with STi-space.

“…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

Demonstratio Mathematica

Abo-Tabl

2020

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.