Abstract
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].
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Zsilinszky, L. Note on hit-and-miss topologies. Rend. Circ. Mat. Palermo 49, 371–380 (2000). https://doi.org/10.1007/BF02904242
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DOI: https://doi.org/10.1007/BF02904242