Refined normality criteria in regionally compact topological domains
Abstract
This manuscript presents enhanced formulations of normality in topological domains, extending the groundwork laid by Williams, Harrington, and others. We propose a novel conceptualization of σ-constrained normality and provide refined conditions for paracompactness in regionally connected, peripherally compact domains. The investigation demonstrates that a regionally compact, regionally connected domain is paracompact if and only if it satisfies our enhanced normality criterion, under cardinal prerequisites milder than those in previous findings. The central result refines the cardinality constraints and division properties associated with Harrington’s outcome on the paracompactness of normal, regionally connected, peripherally compact domains. These methodologies yield stronger constraints compared to Jackson’s inequalities for the case of division axioms in topological settings.
Downloads
References
A. Amourah, J. Oudetallah, I. Batiha, J. Salah, and M. Shatnawi, σ-compact spaces in Nth-topological space, European Journal of Pure and Applied Mathematics, 18 (2) (2025), 5802–5802.
A. Amourah, J. Oudetallah, I. M. Batiha, J. Salah, S. Alsaadi, and T. Sasa, Some types of tri-locally compactness spaces, European Journal of Pure and Applied Mathematics, 18 (2) (2025), 5764–5764.
J. Oudetallah, R. Alharbi, I. Batiha, S. Rawashdeh, and A. Amourah, Some types of tri-Lindelofness spaces, European Journal of Pure and Applied Mathematics, 18 (2) (2025), 5578–5578.
R. Alharbi, J. Oudetallah, M. Shatnawi, and I. M. Batiha, On c-compactness in topological and bitopological spaces, Mathematics, 11 (2023), Article ID 4251.
J. Oudetallah and I. M. Batiha, Mappings and finite product of pairwise expandable spaces, International Journal of Analysis and Applications, 20 (2022), Article ID 66.
J. Oudetallah, N. Abu-Alkishik, and I. M. Batiha, Nigh-open sets in topological space, International Journal of Analysis and Applications, 21 (1) (2023), Article ID 83.
H. A. Shehadeh, I. H. Jebril, X. Wang, S.-C. Chu, and M. Y. I. Idris, Optimal topology planning of electromagnetic waves communication network for underwater sensors using multi-objective optimization algorithms (MOOAs), Automatika, 64 (2) (2023), 315–326.
G. Farraj, B. Maayah, R. Khalil, and W. Beghami, An algorithm for solving fractional differential equations using conformable optimized decomposition method, International Journal of Advances in Soft Computing and Its Applications, 15 (1) (2023).
M. Berir, Analysis of the effect of white noise on the Halvorsen system of variable-order fractional derivatives using a novel numerical method, International Journal of Advances in Soft Computing and Its Applications, 16 (3) (2024), 294–306.
N. R. Anakira, A. Almalki, D. Katatbeh, G. B. Hani, A. F. Jameel, K. S. Al Kalbani, and M. Abu-Dawas, An algorithm for solving linear and non-linear Volterra integro-differential equations, International Journal of Advances in Soft Computing and Its Applications, 15 (3) (2023), 77–83.
R. J. Thompson and A. P. Garrison, A perfectly standard, area-linked, assemblage Holder area that is not assemblage standard using Diamond-star, American Mathematical Monthly, 129 (3) (2022), 245–261.
T. R. Mitchell, Inquiries concerning relationships between standardness conditions and topological attributes, Proceedings of the American Mathematical Society, 148 (4) (2020), 1733–1747.
S. V. Rodriguez, On various relationships of topological domains, Topology and its Applications, 272 (2020), Article ID 107057.
A. P. Garrison, Standard, area-linked, marginally-bounded domains, Transactions of the American Mathematical Society, 374 (1) (2022), 119–135.
R. K. Jensen, Inequalities for subdivision attributes in standard domains, Journal of Pure and Applied Algebra, 223 (6) (2019), 2546–2561.
P. A. Anderson and C. T. Baker, The metrizability of standard, area-linked, marginally-bounded Moore domains, Journal of Mathematical Analysis and Applications, 482 (2) (2021), Article ID 123555.
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
