A guessing principle from a Souslin tree, with applications to topology

Assaf Rinot, Roy Shalev

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We introduce a new combinatorial principle which we call ♣AD. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out de Caux type constructions of topological spaces. Our main result states that strong instances of ♣AD follow from the existence of a Souslin tree. It is also shown that the weakest instance of ♣AD does not follow from the existence of an almost Souslin tree. As an application, we obtain a simple, de Caux type proof of Rudin's result that if there is a Souslin tree, then there is an S-space which is Dowker.

Original languageEnglish
Article number108296
JournalTopology and its Applications
Volume323
DOIs
StatePublished - 1 Jan 2023
Externally publishedYes

Keywords

  • Almost disjoint
  • Club
  • Dowker space
  • Ostaszewski space
  • Souslin line

ASJC Scopus subject areas

  • Geometry and Topology

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