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On hit-and-miss hyperspace topologies

Gerald Beer; Robert K. Tamaki — 1993

Commentationes Mathematicae Universitatis Carolinae

The Vietoris topology and Fell topologies on the closed subsets of a Hausdorff uniform space are prototypes for hit-and-miss hyperspace topologies, having as a subbase all closed sets that hit a variable open set, plus all closed sets that miss (= fail to intersect) a variable closed set belonging to a prescribed family $Δ$ of closed sets. In the case of the Fell topology, where $Δ$ consists of the compact sets, a closed set $A$ misses a member $B$ of $Δ$ if and only if $A$ is far from $B$ in a uniform sense....

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