New types of nearly open sets in topological spaces and their applications

Abstract

In the current study, the idea of $S_{\psi }^{\phi }$-open sets is used to introduce some new types of nearly open sets in topological space, where $\psi =\{\theta ,\delta ,\tau \}$ and $\phi =\{\theta ,\delta ,\tau ,\alpha ,a\}$, thereby illustrating some of their basic qualities and the links between them. Some characterizations, topological properties, mappings, and separation axioms of these new concepts are also presented.

KEYWORDS:

• $S_{\psi }^{\phi }$-open
• $S_{\psi }^{\phi }$-continuity
• $S_{\psi }^{\phi }$-T_i-spaces
• $S_{\psi }^{\phi }$-regular
• $S_{\psi }^{\phi }$-normal spaces

Mathematical subject classifications:

• 54C99
• 54D10
• 54D15
• 54D30
• 54F05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was funded by Taif University, Taif, Saudi Arabia (TU-DSPP-2024-231).