On Metrizability, Completeness and Compactness in Modular Pseudometric Topologies

2025/10/19 by Philani Rodney Majozi, Majozi, Philani Rodney · 1 voice
Mathematics · #18A40 #46E30 #54E35 #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #math.CT #math.GN

paper · pdf · doi:10.48550/arxiv.2510.16787

Abstract

Building on the recent work of Mushaandja and Olela-Otafudu~\citeMushaandjaOlela2025 on modular metric topologies, this paper investigates extended structural properties of modular (pseudo)metric spaces. We provide necessary and sufficient conditions under which the modular topology τ(w) coincides with the uniform topology τ(V) induced by the corresponding pseudometric, and characterize this coincidence in terms of a generalized Δ-condition. Explicit examples are given where τ(w)\subsetneqτ(V), demonstrating the strictness of inclusion. Completeness, compactness, separability, and countability properties of modular pseudometric spaces are analysed, with functional-analytic analogues identified in Orlicz-type modular settings. Finally, categorical and fuzzy perspectives are explored, revealing structural invariants distinguishing modular from fuzzy settings.

Discussions

• Philani Rodney Majozi: On Metrizability, Completeness and Compactness in Modular Pseudometric Topologies https://arxiv.org/abs/2510.16787 https://arxiv.org/pdf/2510.16787 https://arxiv.org/html/2510.1 [bsky, 0 points, 0 comments]

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