English

A classification of the cofinal structures of precompacta

General Topology 2017-01-04 v2 Functional Analysis Logic

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,\bbR)\C(X,\bbR) of continuous real-valued functions on complete metric spaces XX, with respect to the compact-open topology.

Keywords

Cite

@article{arxiv.1607.07669,
  title  = {A classification of the cofinal structures of precompacta},
  author = {Aviv Eshed and M. Vincenta Ferrer and Salvador Hernández and Piotr Szewczak and Boaz Tsaban},
  journal= {arXiv preprint arXiv:1607.07669},
  year   = {2017}
}

Comments

Major revision. Streamlined proofs. Final version, submitted for publication

R2 v1 2026-06-22T15:04:26.380Z