Refined Normality Criteria in Regionally Compact Topological Domains

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.