Let X be a T-1 topological space and Delta a nonempty family of closed subsets of X. We study the hit-and-miss hyperspace topology generated by Delta in terms of its upper and lower parts, focusing on first and second countability and quasi-uniformization. We also obtain some new results on the Vietoris and Fell topologies
Holà, L., Levi, S. (1997). Decomposition properties of hyperspace topologies. SET-VALUED ANALYSIS, 5(4), 309-321 [10.1023/A:1008608209952].
Decomposition properties of hyperspace topologies
Levi, S.
1997
Abstract
Let X be a T-1 topological space and Delta a nonempty family of closed subsets of X. We study the hit-and-miss hyperspace topology generated by Delta in terms of its upper and lower parts, focusing on first and second countability and quasi-uniformization. We also obtain some new results on the Vietoris and Fell topologies
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