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-R0 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 ne...

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Bibliographic Details
Published inRendiconti del Circolo matematico di Palermo Vol. 49; no. 2; pp. 371 - 380
Main Author Zsilinszky, László
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.05.2000
Subjects
Hyperspaces
Topology
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Summary:This is a continuation of [19]. We characterize first and second countability of the general hit-and-miss hyperspace topologyτ+Δ for weakly-R0 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].
ISSN:0009-725X
1973-4409
DOI:10.1007/BF02904242