Strongly quasi-pseudometric aggregation functions are characterized by continuity at zero plus minimal zero preimage for products and by supremum topology conditions for fixed sets.
Beer,Topologies on closed and closed convex sets, vol
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Quasi-pseudometric modular spaces with nonexpansive maps form a category isomorphic to one enriched over a quantale of isotone functions, with matching induced topologies, and quasi-pseudometrizable spaces coincide exactly with those from quasi-pseudometric modulars.
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Strongly quasi-pseudometric aggregation functions
Strongly quasi-pseudometric aggregation functions are characterized by continuity at zero plus minimal zero preimage for products and by supremum topology conditions for fixed sets.
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Quasi-pseudometric modular spaces as $\mathscr{Q}$-categories
Quasi-pseudometric modular spaces with nonexpansive maps form a category isomorphic to one enriched over a quantale of isotone functions, with matching induced topologies, and quasi-pseudometrizable spaces coincide exactly with those from quasi-pseudometric modulars.