Closed products of sets and the axiom of choice.

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. [ABSTRACT FROM AUTHOR]