Properties and Characterizations of k-Continuous Functions and k-Open Sets in Topological Spaces

Abstract

Topology, a branch of mathematics focused on understanding the fundamental properties of spaces, has experienced a new dimension with the introduction of -open sets. This exploration delves into the realm of -topology, unveiling concepts such as -interior, -closure, -limit points, -continuous functions, and more. Through rigorous definitions, illustrative examples, and a web of theorems, the study navigates the intricate relationships between -open sets and traditional topology. We analyze the interplay of -functions, investigate the properties of -homeomorphisms, and discuss the connections between -totally continuous and -contra-continuous functions. By merging established topology with these novel notions, this study sheds light on the intricate fabric of topological spaces (briefly top. sp. ) from a unique perspective. Keywords: Topological Spaces, Homeomorphisms, Contra-Continuous Functions, Totally Continuous