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

Rudin, Mary Ellen

Houston J. Math. 15, No. 2, 255-266 (1989).

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.

Reviewer: H.R.Bennett (Lubbock)

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

Keywords:

hereditarily separable Dowker manifold

Citations:

Zbl 0719.54039