Countable compactness, hereditary π-character, and the Continuum Hypothesis

Abstract

We prove that the Continuum Hypothesis is consistent with the statement that countably compact regular spaces that are hereditarily of countable π-character are either compact or contain an uncountable free sequence. As a corollary we solve a well-known open question by showing that the existence of a compact S-space of size greater than ℵ 1 does not follow from the Continuum Hypothesis.