The complete tunnel axiom
type: Item
instance of: scholarly article
title: The complete tunnel axiom
zbMATH Open document ID: 0652.54018
DOI: 10.1016/0166-8641(88)90052-1
author: Peter Nyikos
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: 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 \(\kappa >\aleph_ 1\).
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 54B15
zbMATH DE Number: 4064026
zbMATH Keywords: Complete Tunnel axiom
zbMATH Keywords: PFA
zbMATH Keywords: MA
Wikidata QID: Q114684105
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90052-1
OpenAlex ID: W2023530696
cites work: Q3220578
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description: scientific article; zbMATH DE number 4064026