The complete tunnel axiom (Q1107163)

The Complete Tunnel axiom (abbreviated: CTA is equivalent to the statement that there is a continuous function from \(\beta\) \(\omega\)- \(\omega\) onto a linearly ordered topological space, such that the preimage of every point has empty interior. In this interesting paper, the author proves that CTA is equivalent to the statement that there is a compactification of \(\omega\) such that the remainder is ordered and no nontrivial sequence from \(\omega\) converges. In addition, he also proves that CTA follows from CH, that PFA implies \(\neg CTA\), and that \(\neg CTA\) is consistent with MA\(+c=\kappa\) for every regular \(\kappa >\aleph_ 1\).