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Countable choice and pseudometric spaces. (English) Zbl 0922.03068
The present paper is a survey about the set-theoretical strength (in the hierarchy of weak choice principles) of various topological assertions about pseudometric spaces. A typical example is Theorem 1.12: The countable choice axiom is equivalent to “Subspaces of separable pseudometric spaces are separable”.
Reviewer’s comment: A pseudometric is like a metric except that the distance of different points may vanish. Nevertheless, the authors’ results do not extend to metric spaces, where the strength of most assertions is not known; cf. P. Howard and J. E. Rubin: Consequences of the axiom of choice (AMS Surveys 59) (1998).
Reviewer: N.Brunner (Wien)

MSC:
03E25 Axiom of choice and related propositions
54E35 Metric spaces, metrizability
54E52 Baire category, Baire spaces
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