Properties related to the first countability of hyperspace topologies (Q2710551)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties related to the first countability of hyperspace topologies |
scientific article |
Statements
2 July 2001
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first countability
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sequentiality
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Vietoris topology
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locally finite topology
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density
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cellularity
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Properties related to the first countability of hyperspace topologies (English)
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The authors, in this interesting paper, give us deeper understanding of hyperspace topologies where sequences play a major rôle. In particular, they provide an example of a space of closed sets with the upper Vietoris topology which is sequential but where its derived set is not countably compact. First countability of the space of closed subsets with the locally finite topology is completely characterized and density and cellularity of this topology are investigated.
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