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Metric spaces and the axiom of choice
Mathematical Logic Quarterly 49 (5):455-466 (2003)
Abstract
We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these mattersMy notes
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2013-11-03
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Citations of this work
Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice.Kyriakos Keremedis, Eleftherios Tachtsis & Eliza Wajch - 2023 - Annals of Pure and Applied Logic 174 (7):103283.
Consequences of the failure of the axiom of choice in the theory of Lindelof metric spaces.Kyriakos Keremedis - 2004 - Mathematical Logic Quarterly 50 (2):141.
Unions and the axiom of choice.Omar De la Cruz, Eric J. Hall, Paul Howard, Kyriakos Keremedis & Jean E. Rubin - 2008 - Mathematical Logic Quarterly 54 (6):652-665.
The axiom of choice in metric measure spaces and maximal $$\delta $$-separated sets.Michał Dybowski & Przemysław Górka - 2023 - Archive for Mathematical Logic 62 (5):735-749.
References found in this work
Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods.David Pincus - 1972 - Journal of Symbolic Logic 37 (4):721-743.
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.
Compact Metric Spaces and Weak Forms of the Axiom of Choice.E. Tachtsis & K. Keremedis - 2001 - Mathematical Logic Quarterly 47 (1):117-128.
Paracompactness of Metric Spaces and the Axiom of Multiple Choice.Paul Howard, K. Keremedis & J. E. Rubin - 2000 - Mathematical Logic Quarterly 46 (2):219-232.
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