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2013, Pro Mathematica
The author introduces a new separation axiom and studies so me of their basic properties. The implication of these new separation axiom among themselves and with the well known axioms semi-T 2 semi-T 1 and semi-T 0 are obtained. l. Introduction 1 Semi-open sets where introduced and investigated by N. Levine [6] in 1963. In 1975, S.N. Maheshwari and R. Prasad [7] used semi-open sets to define and investigate three new separation axioms, called semi-T2o semi-T 1 and semi-T 0. Moreover, they have shown that the following implications hold.
space, 2001
In this paper, we introduce and study a new class of separation axioms called semi-generalized separation axioms using semi-generalized open sets due to Bhattacharya and Lahari. The connections between these separation axioms and other existing well-known related semi separation axioms are also investigated.
Let (X, τ) be a topological space and α, β : P (X) → P (X) be operators associated to τ , we introduce the concept of (α, β)-semi open sets and new generalized forms of separations by (α,β)-semi open sets. Also, we analyze the relations with some well known separation notions.
New trends in mathematical sciences, 2022
In this paper, we study different properties of δ *-semiopen set. We define the concept of δ *-semi generalized closed sets and present some characteristics. In addition, as applications to δ *-semi generalized closed set, we introduce δ *-semi T1 2 space and obtain some of their basic properties. Moreover, we defined the notions of δ *-semi symmetric space, δ *-semi difference sets and δ *-semi kernel of sets, and investigate some of their fundamental properties. At the latest, some new types of spaces are introduced and the relationships of these spaces are studied.
The aim of this paper is to introduce the concept of an operation γ on the class of all semi-generalized open sets in topological spaces. Using this operation, we define a new concept called semi-generalized-γ-open (sg-γ-open) sets and study some of their related properties. We found that the relation between this new concept and sg-open set are independent. In addition, we study some separation axioms called sg-γ-Ti for i = 0, 1, 2. Some basic properties and relations of these separation axioms are obtained.
2013
In this paper, we define some new types of separation axioms in topological spaces by using g b-open set also the concept of g b-R 0 and g b-R 1 are introduced. Several properties of these spaces are investigated.
European Journal of Pure and Applied Mathematics, 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.
IOSR Journals , 2019
In this paper, some new types of separation axioms in topological spaces by using 𝛽g * -open sets are formulated. In particular the concept of 𝛽g * -R0 and 𝛽g * -R1 axioms are introduced. Several properties of these spaces are investigated using these axioms.
In this paper, we introduce two new classes of topological spaces called γ-R0 and γ-R1 spaces in terms of the concept of γ-open sets and investigate some of their fundamental properties.
The aim of this paper is to introduce and study two new classes of spaces, namely rgw⍺lc-𝜏0, rgw⍺lc-𝜏1, rgw⍺lc-𝜏2,rgw⍺lc-regular and rgw⍺lc-normal spaces and obtained their properties by utilizing rgw⍺lc-closed sets. Also we will present some characterizations of these spaces.
In this paper separation axioms of * í µí»¼-closed sets namely *í µí»¼Tc-space, *í µí»¼Tí µí»¼-space, gí µí»¼T*í µí»¼-space, í µí»¼gT*í µí»¼-space and gT*í µí»¼-space are introduced and their properties are analyzed.
European Journal of Pure and Applied Mathematics, 2012
In this paper, we introduce new separations axioms $\Lambda_{r}$-$R_{0}$, $\Lambda_{r}$-$R_{1}$ and $\Lambda_{r}$-$D_{k}$, and study their properties.
2012
In this paper Sp-open sets are used to define some new types of separation axioms in topological spaces. The implications of these separation axioms among themselves with some other separation axioms are obtained. Also their basic properties and characterizations are investigated.
JOURNAL OF EDUCATION AND SCIENCE
Annals of the Alexandru Ioan Cuza University - Mathematics, 2015
In this paper, β-I-open sets are used to define some weak separation axioms and to study some of their basic properties. The implications of these axioms among themselves and with the known axioms are investigated
Boletim da Sociedade Paranaense de Matemática, 2013
This paper introduces gα-D i and gα-R i-spaces using gα-sets and discusses thier properties comprehensively analyzing their relationship. It also derives thier charactrizations interms of gα-continuous and gα-irresolute functions.
2010
The aim of this paper is to introduce some separation axioms, -generalized-semi-R1 space, by utilizing gs-open sets. Further, we investigate some weak separation axioms by using gs-open sets and gs-closure in topological spaces. *2005 Math. Subject classification: 54A05, 54C08.54D10.
2020
The purpose of this paper is to introduce a new type of separation axioms via dense sets, called DTi-spaces (i = 0‚ 1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1), where a DTi-space is a topological space which contains a dense Tisubspace (i = 0‚ 1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1). These new axioms are weaker than the axiom of T1. We provide the basic properties of DTispaces (i = 0‚ 1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1), and we show that the axioms of DT1 4 , DT1 3 , DT1 2 , DT3 4 , DT1 are open hereditary. Moreover, we study the connections between these axioms and the axioms of Ti where (i = 0‚ 1 4 ‚ 1 3 ‚ 1 2 ‚ 3 4 ‚1).
2007
It is the object of this paper to introduce the (1,2) pre-Dk axioms for k = 0, 1, 2.
In this paper, we introduce some types of separation axioms via ω-open sets, namely ω-regular, completely ω-regular and ω-normal space and investigate their fundamental properties, relationships and characterizations. The well-known Urysohn's Lemma and Tietze Extension Theorem are generalized to ω-normal spaces. We improve some known results. Also, some other concepts are generalized and studied via ω-open sets.
Journal of emerging technologies and innovative research, 2021
The aim of this paper is to introduce and study some new types of separation axioms such as -T0, -T1, -T2, -R0 and -R1 axioms in topological spaces by using -open set. The relationships among -T0, -T1, -T2 and some other separation axioms are investigated.
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