Turkish Journal of Mathematics
Abstract
This paper explores the notions of $\delta\beta^*$-${\mathfrak{I}}$-submaximality and $\delta\beta^*$-${\mathfrak{I}}$-paracompactness within ideal topological spaces, viewing them as natural generalizations of the traditional concepts of submaximality and paracompactness. These concepts arise naturally in the context of ideal topology, where an ideal $\mathfrak{I}$ on a topological space provides additional structure for analyzing topological properties. It focuses on the study of submaximal spaces by employing $\delta\beta^*$-${\mathfrak{I}}$-open sets, which serve as fundamental building blocks for understanding the topological behavior in ideal spaces. Furthermore, the work provides multiple characterizations of $\delta\beta^*$-${\mathfrak{I}}$-paracompact spaces and examines how this property behaves under various types of mappings. The results establish important connections between classical topological properties and their ideal counterparts, contributing to the growing theory of ideal topological spaces.
DOI
10.55730/1300-0098.3677
Keywords
Ideal topological space, generalized open set, submaximality, paracompactness
First Page
709
Last Page
730
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
BOONPOK, C, & SAMA-AE, A (2026). Generalized submaximality and paracompactness in ideal topological spaces via δβ*-𝔍-open sets. Turkish Journal of Mathematics 50 (4): 709-730. https://doi.org/10.55730/1300-0098.3677
