Theta^omega-Open Set and its Corresponding Topological Concepts

Abstract

In this paper, we introduce a different version of open set called $\theta^\omega$-open set, and then described its connection to the other well-known concepts such as the classical open, $\theta$-open, and $\omega$-open sets. It is worth noting that the family of all $\theta^\omega$-open sets forms a topology. We also define and investigate the concepts of $\theta^\omega$-interior and $\theta^\omega$-closure of a set.  The concepts of strongly $\theta^\omega$-open function, strongly $\theta^\omega$-closed function, $\theta^\omega$-open function, and $\theta^\omega$-closed function are defined and characterized. Finally, related concepts such as $\theta^\omega$-continuous function, strongly \T-continuous function, and $\theta^\omega$-connected are investigated further.