Generalized Prime Systems from a Topological Perspective

Document Type : Original Article

Authors
Ahmed B. AL-Nafee
Faez AL-Maamori
Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon 51002, Iraq.
10.24271/psr.2025.514762.2056
Abstract
Abstract
This study focuses on developing a topological framework for studying a generalized prime system (GPS), based on constructing specialized topological spaces determined by such systems (GPS-determined topological spaces). The research demonstrates how nested open sets and discrete thresholds govern the distribution and asymptotic behavior of generalized primes. The main contributions include a complete topological characterization of generalized prime counting functions, systematic methods for constructing generalized primes, and a concrete example illustrating the practical application of these theoretical results. This work enriches traditional analytical approaches by introducing new topological tools, opening promising interdisciplinary research avenues in number theory and topology.
Keywords
Topological characterization
Generalized prime
topological spaces
GPS-determined topological spaces
Crossmark
Subjects
Passer Journal of Basic and Applied Sciences
Volume 7, Issue 2
December 2025
Pages 759-764