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On countable products of finite Hausdorff spaces. (English) Zbl 0959.03033
It is well known that Tikhonov’s product theorem and the Axiom of Choice are equivalent propositions. This paper presents further (localized) versions of this for countable families of finite sets (with the discrete topology). The Axiom of Choice for such families is equivalent to Tikhonov’s theorem for them and to the Baire Category theorem for their products. A local version of this states that for every \(n\) the Axiom of Choice for sequences of at most \(n\)-element sets is equivalent to the compactness (or the Baire Category theorem) for products of sequences of at most \(n+1\)-element sets.
Reviewer: K.P.Hart (Delft)

03E25 Axiom of choice and related propositions
54B10 Product spaces in general topology
54A35 Consistency and independence results in general topology
54D30 Compactness
54E52 Baire category, Baire spaces
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