Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces

M Arunmaran,K Kannan

doi:10.1155/2018/7863713

Abstract

We are going to establish some results of τ1τ2-δ semiconnectedness and compactness in a bitopological space. Besides, we will investigate several results in τ1τ2-δ semiconnectedness for subsets in bitopological spaces. In particular, we will discuss the relationship related to semiconnectedness between the topological spaces and bitopological space. That is, if a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected, then the topological spaces (X,τ1) and (X,τ2) are δ-semiconnected. In addition, we introduce the result which states that a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected if and only if X and ϕ are the only subsets of X which are τ1τ2-δ semiclopen sets. Moreover, we have proved some results in compactness also. Altogether, several results of τ1τ2-δ semiconnectedness and compactness in a bitopological space have been discussed.

Highlights

The concept “bitopological space” was established by Kelly in [1]
We introduce the result which states that a bitopological space (X, τ1, τ2) is τ1τ2-δ semiconnected if and only if X and φ are the only subsets of X which are τ1τ2-δ semiclopen sets
He introduced this concept in his journal of London Mathematical Society in 1963

Summary

Introduction

The concept “bitopological space” was established by Kelly in [1]. He introduced this concept in his journal of London Mathematical Society in 1963. He initiated his study about bitopological space by using quasimetric and its conjugate. Every metric space is a topological space. Maheshwari and Prasad [2] introduced semiopen sets in bitopological spaces in 1977. Edward Samuel and Balan [6] established the concept τ1τ2-δ semiopen sets in bitopological spaces. We have already published some properties of τ1τ2-δ semiopen/closed sets in bitopological spaces in [7]. We are going to discuss the following results:

Methods

Results

Conclusion