On Generalized β-Open Sets in Ideal Bitopological Space

AL-Rafidain Journal of Computer Sciences and Mathematics

In this paper, we define ii-open set in bitopological space as follows: Let (, 1 , 2) be a bitopological space, a subset A of is said to be (1 2ii-open set) if there exist U,V ≠ ∅ , and U,V ∈ 1 ∪ 2 such that: 1. A=int 1 (U) or A=int 2 (V) 2. A⊆ 1 (∩) or A⊆ 2 (∩) We study some characterizations and properties of this class. Also, we explain the relation between ii-open sets and open sets, i-open sets and α-open sets in bitopological space. Furthermore, we define ii-continuous mapping on bitopological spaces with some properties.

viXra, 2020

In this paper we introduce and characterize the concepts of β-open sets and their related notions in ideal bitopological spaces.

In this paper, we introduce some properties of τ1τ2 − δ semi open sets / closed sets in a bitopological space. With that, we investigate several results in τ1τ2 − δ semi open sets / closed sets and τ1τ2 − δ semi continuous in bitopological spaces. Further, we prove some results in τ2τ1 − δ semi open sets / closed sets in bitopological spaces. Bitopological space does not exist for every metric space. But it exists for special type of metric spaces,called as " asymmetric metric spaces ". Bitopological spaces have some applications in various parts in mathematics. Moreover, a high level of modern knowledge of bitopological spaces theory has made it possible to introduce and study algebra of new type the corresponding representation of which brings one to the special class of bitopological spaces. Key Words: τ1τ2 − δ semi open sets, τ1τ2 − δ semi closed sets, τ1τ2 − δ semi continuous

2018

The aim of this paper is to introduced and characterized the concepts of α-open sets and their related notions in ideal bitopological spaces.

viXra, 2020

The aim of this paper is to introduced and characterized the concepts of semiopen sets and their related notions in ideal bitopological spaces. 2000 Mathematics Subject Classification. 54D10.

Journal of Advanced Studies in Topology, 2015

In this paper we introduced two new classes of sets in bitopological spaces, the first type is weaker than ij-Ωclosed sets namely, ij-Ω *-closed sets, and the second type called ij-Ω * *-closed sets which lies between the class of ij-Ω-closed sets and the class of ij-g-closed sets. We find some basic properties and applications of these sets. We also, introduce new bitopological separation axioms and new type of continuous functions between bitopological spaces. Finally, we prove that some of the introduced bitopological separation properties are preserved under some types of continuous functions.

viXra, 2020

The aim of this paper is to introduced and characterized the concepts of α-open sets and their related notions in ideal bitopological spaces. 2000 Mathematics Subject Classification. 54D10. Key words and phrases. Ideal bitopological spaces, (1, 2)-α-I-open sets, (1, 2)α-I-closed sets.

The purpose of this paper is to introduce and study the properties of (1,2) γopen set in bitopological space .In this paper we also study (

In this paper, we introduce and study the notions of S γ 1 -open sets, S γ 1continuous and 12-almost S γ 1 -continuous functions in bitopological space. We also investigated the fundamental properties of such functions.

IOSR Journal of Mathematics, 2013

The purpose of this paper is to introduce and study the properties of (1,2) γopen set in bitopological space .In this paper we also study and and γ-open set .

Tamkang Journal of Mathematics, 2012

In this paper, we introduce and define a new class of sets, called S ı-open sets, in bitopological spaces. By using this set, we introduce and define the notion of S ı-continuity and investigate some of its properties. In particular, S ı-open sets and S ıcontinuity are used to extend some known results of continuity.

Boletim da Sociedade Paranaense de Matemática, 2011

The aim of this paper is to introduce and characterize the concepts of preopen sets and their related notions in ideal bitopological spaces.

International journal of scientific research in mathematical and statistical sciences, 2018

The concept of bitopological space was first introduced by J.C.Kelly in 1963 (i.e) a non-empty set equipped with two arbitrary topologies and .The concept of generalized closed sets plays a significant role in general topology and these are the research topics of many Topologists worldwide.In 1970 Norman Levine introduced the concept of generalization of closed sets in topological spaces and he defined the semi-open sets and semi-continuity in bitopological spaces. In this paper we introduce a new class of generalized closed sets namely (i,j)-closed sets in bitopological spaces ()a subset of a bitopological space () is called ()-closed if-() ,whenever , is-open in () and some of the properties were discussed. The class of (i,j)-closed sets settled in between the class of (i,j)-closed sets and the class of (i,j)-gs-closed sets.Some of the basic properties of (i,j)-closed sets are investigated.

Mathematical theory and modeling, 2013

In this paper, we apply the notion of qpI-open sets and qpI-continuous functions to present and study a new class of functions called contra qpI-continuous functions in ideal bitopological spaces. Keywords: Ideal bitopological space, qpI-open sets, qpI-continuous functions, qpI -irresolute functions.

Proyecciones (Antofagasta), 2014

In this paper we introduce a new class of generalized closed sets in bitopological space using local function, two extension operators and semi-open sets. We have also investigated some properties in subspace bitopology defining kernel and image.