I- Continuous Functions in Ideal Bitopological Spaces

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.

AL-Rafidain Journal of Computer Sciences and Mathematics

In this paper, we defined i-open sets and i-star generalized w-closed sets in bitopological spaces) , , (2 1   X by using the definition of i-open sets in topological space ()  , X (see[6]). We present some fundamental properties and relations between these classes of sets, further we give examples to explain these relations.

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.

Acta Scientiarum. Technology, 2013

In this article we introduce the notion of weakly b-continuous functions in bitopological spaces as a generalization of b-continuous functions. We prove several properties of these functions. AMS Classification No : 54A10; 54C10; 54C08; 54D15.

We continue the study of bitopological separation axioms that was begun by Kelly and obtain some results. Furthermore, we introduce a concept of pairwise Lindelöf bitopological spaces, namely, p 2 -Lindelöf spaces, and their properties are established. We also show that p 2 -Lindelöf is not a hereditary property. Finally, we show that p 2 -Lindelöf is a p 2 -topological property.

Baghdad Science Journal, 2020

This work, introduces some concepts in bitopological spaces, which are nm-j-ω-converges to a subset, nm-j-ω-directed toward a set, nm-j-ω-closed mappings, nm-j-ω-rigid set, and nm-j-ω-continuous mappings. The mainline idea in this paper is nm-j-ω-perfect mappings in bitopological spaces such that n = 1,2 and m =1,2 n ≠ m. Characterizations concerning these concepts and several theorems are studied, where j =  , δ,  , pre, b, .

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.

International Journal of Science and Research (IJSR), 2015

In this paper we extend the concept of α-local function due to W. Al-omeri, Mohd. Salmi, Md. Noorani and A. Al-omari [1] to ideal bitopological spaces and study some of its properties. Further the concepts of qαI-open sets and qαI-continuous mappings are introduced and studied.

2014

In this paper we study the notion of connectedness in ideal bitopological spaces. AMS Mathematics Subject Classification (2000): 54A10, 54A05, 54A20

Acta Scientiarum-technology, 2013

In this article we introduce the notion of weakly b-continuous functions in bitopological spaces as a generalization of b-continuous functions. We prove several properties of these functions.