On metrizability, completeness and compactness in modular pseudometric topologies

Building on the recent work of Mushaandja and Olela-Otafudu [10] 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 ) ⊊ τ ( 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.