Note on hit-and-miss topologies

This is a continuation of [19]. We characterize first and second countability of the general hit-and-miss hyperspace topologyτ ₊ ^Δ for weakly-R ₀ base spaces. Further, metrizability ofτ ₊ ^Δ is characterized with no preliminary conditions on the base space and the generating family of closed sets and a new proof on uniformizability (i.e. complete regularity) ofτ ₊ ^Δ is given in this general setting, thus generalizing results of [3], [5] and [6].