On the extension of $SD$ sets by using generalized open sets in bitopological spaces

Document Type : Research Paper


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


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.


Volume 14, Issue 1
January 2023
Pages 1627-1638
  • Receive Date: 22 July 2022
  • Revise Date: 03 October 2022
  • Accept Date: 09 October 2022