Countable choice and pseudometric spaces
type: Item
instance of: scholarly article
title: Countable choice and pseudometric spaces
zbMATH Open document ID: 0922.03068
DOI: 10.1016/S0166-8641(97)00138-7
author: H. Lamar Bentley
author: Horst Herrlich
published in: Topology and its Applications
publication date: 1999-10-18T00:00:00Z
review text: The present paper is a survey about the set-theoretical strength (in the hierarchy of weak choice principles) of various topological assertions about pseudometric spaces. A typical example is Theorem 1.12: The countable choice axiom is equivalent to ``Subspaces of separable pseudometric spaces are separable''. Reviewer's comment: A pseudometric is like a metric except that the distance of different points may vanish. Nevertheless, the authors' results do not extend to metric spaces, where the strength of most assertions is not known; cf. \textit{P. Howard} and \textit{J. E. Rubin}: Consequences of the axiom of choice (AMS Surveys 59) (1998).
Mathematics Subject Classification ID: 03E25
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 1307988
zbMATH Keywords: axiom of choice
zbMATH Keywords: compactness
zbMATH Keywords: Baire category
zbMATH Keywords: separability
zbMATH Keywords: survey
zbMATH Keywords: hierarchy of weak choice principles
zbMATH Keywords: pseudometric spaces
zbMATH Keywords: countable choice
reviewed by: Norbert Brunner
MaRDI profile type: Publication
cites work: Q4353276
cites work: A remark on the axiom of choice
cites work: The axiom of choice
cites work: Q3960633
full work available at URL: s0166-8641(97)00138-7
OpenAlex ID: W2022172691
description: scientific article; zbMATH DE number 1307988