Document Type : Research Paper

Authors

• Necati Can Açıkgöz
• Ceren Sultan Elmalı

Department of Mathematics, Erzurum Technical University, Yakutiye, 25050, Turkey

Abstract

In this paper, we introduce and study $ij$-somewhere dense sets in bitopological spaces. We present $ij$-somewhere density properties by using some generalized open sets which are used for generalizing the operators of interior, closure and boundary. In this manner, we also investigate several properties of $ij$-somewhere dense sets and present several examples for the main results. We also introduce $\omega$-hyperconnectedness as an extension of hyperconnectedness by using $ij$-somewhere dense sets. We later present some separation axioms based on these types of sets.

Keywords

• bitopological spaces
• $ij$-somewhere dense sets
• generalized open sets
• hyperconnected space