A ZFC Dowker space in ${\aleph }_{\omega +1}$: an application of pcf theory to topology

Abstract

A ZFC Dowker space is constructed which has cardinality ${\aleph }_{\omega +1}$. This provides a bound in ZFC to the first cardinal in which there is a ZFC Dowker space. The space we construct is a closed and cofinal subspace of M.~E.~Rudin's Dowker space from 1971. A theorem from pcf theory used in the proof, but otherwise the proof is elementary.