Abstract
We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we classify the cofinal structure of local bases in the groups C(X,R) of continuous real-valued functions on complete metric spaces X, with respect to the compact-open topology.
Original language | English |
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Article number | 102810 |
Journal | Annals of Pure and Applied Logic |
Volume | 171 |
Issue number | 8 |
DOIs | |
State | Published - 1 Aug 2020 |
Bibliographical note
Publisher Copyright:© 2020 Elsevier B.V.
Keywords
- Compact sets
- Compact-open topology
- Local density
- Precompact sets
- Tukey equivalence