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The Compactness of 2 ℝ and the Axiom of Choice
Author(s) -
Keremedis Kyriakos
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 - 10.1002/1521-3870(200010)46:4<569::aid-malq569>3.0.co;2-j
Subject(s) - axiom of choice , mathematics , compact space , tychonoff space , axiom , product (mathematics) , space (punctuation) , pure mathematics , discrete mathematics , combinatorics , hausdorff space , set (abstract data type) , set theory , computer science , geometry , programming language , operating system
We show that for every we ordered cardinal number m the Tychonoff product 2 m is a compact space without the use of any choice but in Cohen's Second Mode 2 ℝ is not compact.