Rudin-type Dowker spaces
Keywords:
Dowker spaces, Rudins space, pcf theory, Shelah's Strong HypothesisAbstract
A construction scheme of topological spaces, which generalizes M. E. Rudin's construction of a Dowker space in ZFC, is given, and is shown to produce a proper class of Dowker spaces. A proper subclass of this class of spaces are provably collectionwise normal Dowker in ZFC alone. The theory ZFC + SSH, where SSH is Shelah's Strong Hypothesis, proves that the whole class consists of collectionwise normal Dowker spaces. Whether all members of this class are Dowker in ZFC is still open.
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