Nano Ideal Semi Alpha Generalized Continuous and Irresolute Mappings in Nano Ideal Topological Spaces

Abstract

Topology, though relatively recent in its development, has found remarkable applications across nearly all fields. While the theoretical or fundamental aspects of topology may seem abstract or dry at first, its applied side becomes truly fascinating once one becomes familiar with it. This research explores a variety of applications in diverse areas of Science and Technology-including Biology, Robotics, Geographic Information Systems (GIS), Engineering, Computer Science, and the Medical field. Though topology originates from mathematics, its influence extends far beyond, making a profound impact on numerous disciplines with its powerful and wide-ranging applications. The purpose of this paper is to present another class of functions referred to as Nano ideal semi α-generalized continuous maps, NIsαɡ-irresolute maps, NIsαɡ-open maps, NIsαɡ-closed maps, strongly NIsαɡ-open maps, strongly NIsαɡ-closed maps, NIsαɡ-homeomorphisms, Nano quasi Isαɡ-open maps, and Nano quasi Isαɡ-closed maps in nano ideal topological spaces. We investigate several properties and characterizations of this class of mappings in nano-ideal topological spaces.