@article{Alshammari2026, 
author = {Ibtesam Alshammari},
title = {Ideal topological approaches to hyperconnected and irresolvable spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {7066-7077},
keywords = {ideal topological space, ω-open set, ω~-dense, ω~-hyperconnected, ω~-resolvable, ω~-irresolvable, ω-irresolvable},
url = {https://www.sciopen.com/article/10.3934/math.2026290},
doi = {10.3934/math.2026290},
abstract = {In this paper, we presented a systematic study of several new notions in the setting of ideal topological spaces, such as              ω      ~      -dense sets,              ω      ~      -hyperconnectedness, strongly              ω      ~      -hyperconnectedness, and resolvability-type concepts. By employing    ω-open sets together with              ω      ~      -local functions, we established fundamental properties, explored the relationships among these notions, and demonstrated how they extend and refine classical concepts in general topology.}
}