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Consequences of the failure of the axiom of choice in the theory of Lindelof metric spaces

Kyriakos Keremedis

Mathematical Logic Quarterly 50 (2):141 (2004)

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Metric spaces and the axiom of choice.Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2003 - Mathematical Logic Quarterly 49 (5):455-466.details We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters. Download Export citation Bookmark 4 citations
(1 other version)Products of compact spaces in the least permutation model.Norbert Brunner - 1985 - Mathematical Logic Quarterly 31 (25‐28):441-448.details Download Export citation Bookmark 5 citations
Products of compact spaces and the axiom of choice II.Omar De la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2003 - Mathematical Logic Quarterly 49 (1):57-71.details This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces . We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products. Download Export citation Bookmark 4 citations
(1 other version)Products of Compact Spaces in the Least Permutation Model.Norbert Brunner - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (25-28):441-448.details Download Export citation Bookmark 5 citations
The failure of the axiom of choice implies unrest in the theory of Lindelöf metric spaces.Kyriakos Keremedis - 2003 - Mathematical Logic Quarterly 49 (2):179-186.details In the realm of metric spaces the role of choice principles is investigated. Download Export citation Bookmark 4 citations

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