Rough Convergence of Nets
DOI:
https://doi.org/10.29304/jqcsm.2025.17.42530Keywords:
Rough Topological space, Rough-Open Set, Rough exceptional setAbstract
This paper investigates fundamental and advanced concepts in rough topology by extending classical topological notions through the lens of rough set theory. We define and analyze rough-open and rough-closed sets, rough convergence of nets and filters, rough cluster and limit points, and separation axioms in rough spaces. The study introduces new forms of continuity such as rough-continuity, rough-irresoluteness, and rough-proper functions, and explores their interactions with compactness and convergence. Several illustrative examples and theorems are provided to demonstrate how rough approximations influence topological structure and behavior. The results generalize classical convergence theory and offer a unified framework for studying indiscernibility-based topology.
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Copyright (c) 2025 Ruqaya Nameer Abd Ali , Sattar Hameed Hamzah
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
