Exploring Nano Simply Open Sets in Nano Topology: Applications and Insights - El Sayed, M. (Journal of Applied Science, Engineering, Technology, and Education, 2025)
In recent times, nano set theory has shown broad applications in addressing practical challenges in various domains, including engineering, social sciences, and healthcare sciences. The notion of nano topological spaces, along with associated concepts like nano near open sets, has greatly developed because of its practical usefulness. The idea of nano continuity extends the idea of continuity. Likewise, nano open sets extend the notion of open sets within topological spaces. This paper presents a new class of nano near open sets, termed "nano simply open sets" and "nano delta sets," which expands and alters the current concepts of nano open sets (and, in certain instances, nano near open sets). We introduce a novel category of nano simply open sets, explore their characteristics, and analyze their connections with other sets. Additionally, we investigate new ideas like "nano simply continuous functions” and also, we introduce new notions of continuity based on the new notions. We shall study some of their properties and we will study the relationship between the new concepts and various other nano open sets.