Research Paper
Year: 2023 | Month: July-September | Volume: 8 | Issue: 3 | Pages: 405-425
DOI: https://doi.org/10.52403/ijshr.20230355
Properties and Characterizations of k-Continuous Functions and k-Open Sets in Topological Spaces
Ahmed M. Rajab1, Hawraa S. Abu Hamd2, Eqbal N. Hameed3
1,2Department of Mathematics,
Faculty Of Computer Sciences and Mathematics, University of KUFA, Kufa, Najaf, IRAQ
Faculty Of Education, University of KUFA, Kufa, Najaf, IRAQ
Corresponding Author: Ahmed M. Rajab
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