A classification of the cofinal structures of precompacta

Aviv Eshed; M. Vicenta Ferrer; Salvador Hernandez; Piotr Szewczak; Boaz Tsaban

doi:10.1016/j.apal.2020.102810

A classification of the cofinal structures of precompacta

Aviv Eshed, M. Vicenta Ferrer, Salvador Hernandez, Piotr Szewczak, Boaz Tsaban

Weizmann Institute of Science, Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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. (C) 2020 Elsevier B.V. All rights reserved.

Original language	English
Article number	102810
Number of pages	15
Journal	Annals of Pure and Applied Logic
Volume	171
Issue number	8
Early online date	8 Apr 2020
DOIs	https://doi.org/10.1016/j.apal.2020.102810
State	Published - 1 Aug 2020

Keywords

Compact sets
Compact-open topology
Local density
Precompact sets
Tukey equivalence

All Science Journal Classification (ASJC) codes

Logic

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10.1016/j.apal.2020.102810

https://arxiv.org/abs/1607.07669License: Other

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AU - Hernandez, Salvador

AU - Szewczak, Piotr

AU - Tsaban, Boaz

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AB - 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. (C) 2020 Elsevier B.V. All rights reserved.

KW - Compact sets

KW - Compact-open topology

KW - Local density

KW - Precompact sets

KW - Tukey equivalence

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M3 - مقالة

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JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

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M1 - 102810

ER -

A classification of the cofinal structures of precompacta

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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