Countable choice and pseudometric spaces (Q1295287)

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. \textit{P. Howard} and \textit{J. E. Rubin}: Consequences of the axiom of choice (AMS Surveys 59) (1998).