@article{Aydın2025, 
author = {Tuğçe Aydın},
title = {Refining and extending the theoretical foundations of    r-near topology},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {30429-30459},
keywords = {near sets, r-near topology, r-near open sets, r-near accumulation points, r-near boundary points},
url = {https://www.sciopen.com/article/10.3934/math.20251335},
doi = {10.3934/math.20251335},
abstract = {The present paper aims to refine and extend the theoretical foundations of    r-near topology. For this reason, it first redefines the concept of    r-near neighborhoods to address inconsistencies in previous studies and clarifies the relationship between    r-near open neighborhoods and    r-near closure. This study then elaborates on the fundamental properties of    r-near closed sets,    r-near interior,    r-near closure, and    r-near neighborhoods. Subsequently, it introduces four novel concepts within    r-near topology:    r-near accumulation points,    r-near isolated points,    r-near exterior points, and    r-near boundary points. Furthermore, this study explores some of their basic properties and provides illustrative examples regarding the aforesaid concepts. Additionally, it researches the relationships between    r-near interior,    r-near closure, and    r-near exterior in the    r-near topological spaces and their classical topological counterparts. Lastly, the study highlights the theoretical significance of    r-near topology and suggests potential directions for further research.}
}