Ideal topological approaches to hyperconnected and irresolvable spaces

In this paper, we presented a systematic study of several new notions in the setting of ideal topological spaces, such as $\tilde{\omega }$-dense sets, $\tilde{\omega }$-hyperconnectedness, strongly $\tilde{\omega }$-hyperconnectedness, and resolvability-type concepts. By employing $\omega$-open sets together with $\tilde{\omega }$-local functions, we established fundamental properties, explored the relationships among these notions, and demonstrated how they extend and refine classical concepts in general topology.