Quasi-metrizability of a topological space X is equivalent to the availability on X of a decreasing neighbourhood base (x) n at every x X, so constituted that, for every countable and relatively locally finite A X and n ω (writing, for each B X and each m ω, (B) m for {(x) m : x B}), we have ((A) ν ) ν (A) n for some ν ω (dependent on A and n). By comparison, metrizability of T 0 -spaces X is equivalent to the availability on X of a decreasing sequence (x) n of neighbourhoods at every x X, so constituted that, for every A X, we have {(A) n : n ω} = ClA = {Cl(A) n : n ω} (Hung, 1977).