Compactness and the axiom of choice
type: Item
instance of: scholarly article
title: Compactness and the axiom of choice
zbMATH Open document ID: 0881.54026
DOI: 10.1007/BF00124110
published in: Applied Categorical Structures
publication date: 1998-02-01T00:00:00Z
review text: Four versions of compactness (equivalent in ZFC) and their properties are investigated without the axiom of choice. All the four versions are equivalent iff the axiom of choice holds (many equivalent forms concerning mainly products of spaces are given). The Boolean prime ideal theorem holds iff the compactness defined by open covers is equivalent to compactness defined by convergence of ultrafilters (or to compactness of completely regular spaces defined as closed subspaces of Tychonov cubes). The last case and some more other cases are again accompanied by several equivalent forms for products or compactifications.
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 03E25
Mathematics Subject Classification ID: 54B10
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 1053685
zbMATH Keywords: compactness
zbMATH Keywords: axiom of choice
zbMATH Keywords: cartesian product
Wikidata QID: Q114018505
author: Horst Herrlich
reviewed by: M. Hušek
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1053685