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Countable sums and products of metrizable spaces in ZF
Author(s) -
Keremedis Kyriakos,
Tachtsis Eleftherios
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200410011
Subject(s) - mathematics , metrization theorem , axiom of choice , tychonoff space , countable set , disjoint sets , metric space , product (mathematics) , separation axiom , axiom , topological space , discrete mathematics , pure mathematics , separable space , set theory , set (abstract data type) , mathematical analysis , computer science , geometry , programming language
Abstract We study the role that the axiom of choice plays in Tychonoff's product theorem restricted to countable families of compact, as well as, Lindelöf metric spaces, and in disjoint topological unions of countably many such spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)