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

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