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On Lindelöf Metric Spaces and Weak Forms of the Axiom of Choice
Author(s) -
Keremedis Kyriakos,
Tachtsis Eleftherios
Publication year - 2000
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/(sici)1521-3870(200001)46:1<35::aid-malq35>3.0.co;2-g
Subject(s) - mathematics , axiom of choice , countable set , metric space , separable space , axiom , metric (unit) , statement (logic) , pure mathematics , space (punctuation) , discrete mathematics , base (topology) , mathematical analysis , set (abstract data type) , set theory , computer science , geometry , operations management , political science , law , economics , programming language , operating system
We show that the countable axiom of choice CAC strictly implies the statements “Lindelöf metric spaces are second countable” “Lindelöf metric spaces are separable”. We also show that CAC is equivalent to the statement: “If ( X , T ) is a Lindelöf topological space with respect to the base ℬ, then ( X , T ) is Lindelöf”.