Ideal topological approaches to hyperconnected and irresolvable spaces

Ibtesam Alshammari; Ibtesam Alshammari

doi:10.3934/math.2026290

AIMS Mathematics

2026, Volume 11, Issue 3: 7066-7077. doi: 10.3934/math.2026290

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Research article

Ideal topological approaches to hyperconnected and irresolvable spaces

Ibtesam Alshammari ^,

Department of Mathematics, College of Science, University of Hafr Al Batin, Hafr Al Batin, Saudi Arabia

Received: 11 January 2026 Revised: 19 February 2026 Accepted: 04 March 2026 Published: 18 March 2026
MSC : 54A05, 54A10

In this paper, we presented a systematic study of several new notions in the setting of ideal topological spaces, such as $ \widetilde{\omega} $-dense sets, $ \widetilde{\omega} $-hyperconnectedness, strongly $ \widetilde{\omega} $-hyperconnectedness, and resolvability-type concepts. By employing $ \omega $-open sets together with $ \widetilde{\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.
Citation: Ibtesam Alshammari. Ideal topological approaches to hyperconnected and irresolvable spaces[J]. AIMS Mathematics, 2026, 11(3): 7066-7077. doi: 10.3934/math.2026290

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Abstract

In this paper, we presented a systematic study of several new notions in the setting of ideal topological spaces, such as $ \widetilde{\omega} $-dense sets, $ \widetilde{\omega} $-hyperconnectedness, strongly $ \widetilde{\omega} $-hyperconnectedness, and resolvability-type concepts. By employing $ \omega $-open sets together with $ \widetilde{\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.

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