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TWO TOPOLOGICAL EQUIVALENTS OF THE AXIOM OF CHOICE
Author(s) -
Schechter Eric,
Schechter E.
Publication year - 1992
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.19920380152
Subject(s) - mathematics , axiom of choice , axiom , product (mathematics) , closure (psychology) , topological space , constructive set theory , product topology , topology (electrical circuits) , separation axiom , axiom independence , urelement , zermelo–fraenkel set theory , discrete mathematics , combinatorics , computer science , set (abstract data type) , geometry , set theory , economics , market economy , programming language
We show that the Axiom of Choice is equivalent to each of the following statements: (i) A product of closures of subsets of topological spaces is equal to the closure of their product (in the product topology); (ii) A product of complete uniform spaces is complete.