Compact C-spaces and S-spaces
Part of the Lecture Notes in Mathematics book series (LNM, volume 609)
We introduce a set theoretic axiom which is weaker than as well as axiom F. Using (CH) and we prove the existence of a locally compact, T2, locally countable, first countable, hereditarily separable, sequentially compact non-compact space X. The one point compactification X* of X is a compact, T2, C-space (meaning X* is of countable tightness) which is not sequential. We also construct a compact, T2, C-space Y which is not sequential using only the continuum hypothesis (CH). This solves some well known problems on S-spaces and also on compact C-spaces under least set theoretic axioms.
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