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 language | English |
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Article number | 108296 |
Journal | Topology and its Applications |
Volume | 323 |
DOIs | |
State | Published - 1 Jan 2023 |
Externally published | Yes |
Keywords
- Almost disjoint
- Club
- Dowker space
- Ostaszewski space
- Souslin line
ASJC Scopus subject areas
- Geometry and Topology