Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces. (2nd May 2018)

• Record Type: Journal Article
• Authors: Arunmaran, M.; Kannan, K.
• Other Names: Papadopoulos Basil K. Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2018(2018)
• Publication Date: 2018-05-02
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2018/7863713
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : We are going to establish some results of τ 1 τ 2 -δ semiconnectedness and compactness in a bitopological space. Besides, we will investigate several results in τ 1 τ 2 -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, τ 1, τ 2 ) is τ 1 τ 2 -δ semiconnected, then the topological spaces ( X, τ 1 ) and ( X, τ 2 ) are δ -semiconnected. In addition, we introduce the result which states that a bitopological space ( X, τ 1, τ 2 ) is τ 1 τ 2 -δ semiconnected if and only if X and ϕ are the only subsets of X which are τ 1 τ 2 -δ semiclopen sets. Moreover, we have proved some results in compactness also. Altogether, several results of τ 1 τ 2 -δ semiconnectedness and compactness in a bitopological space have been discussed.