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Abstract

With a slight modification of a previous argument due to Schechter, we show that the Axiom of Choice is equivalent to the following topological statement: “If a product of a non-empty family of sets is closed in a topological (Tychonoff) product, then at least one of the factors is closed”. We also discuss the case on which one adds the hypothesis that the closed product of sets is a non-empty set.

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(Warszawa, 1977 ). [3] Sorgenfrey , R. H. 1947 On the topological product of paracompact spaces Bull. Amer. Math. Soc

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Tkachenko , M., Embedding paratopological groups into topological products, Topology Appl. , 156 (2009), 1298–1305. Tkachenko M. Embedding paratopological groups into topological

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