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Countable sums and products of Loeb and selective metric spaces. (English) Zbl 1121.03063

Summary: We investigate the role that weak forms of the axiom of choice play in countable Tychonoff products, as well as countable disjoint unions, of Loeb and selective metric spaces.

MSC:

03E25 Axiom of choice and related propositions
54A35 Consistency and independence results in general topology
54D45 Local compactness, \(\sigma\)-compactness
54E35 Metric spaces, metrizability
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