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Countable point separating open covers for manifolds. (English) Zbl 0719.54040

This paper gives an extremely sophisticaed example of a hereditarily separable Dowker manifold which has a countable point-separating open cover. \(ZFC+\blacklozenge\) is needed and clever geometric arguments are used. Using MA plus the negation of the continuum hypothesis Z. Balog and the reviewer [see the preceding review] have shown that all such manifolds of weight \(<c\) are metrizable.

MSC:

54E35 Metric spaces, metrizability
57N99 Topological manifolds
54A35 Consistency and independence results in general topology
03E35 Consistency and independence results
03E50 Continuum hypothesis and Martin’s axiom

Citations:

Zbl 0719.54039
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