Reflecting Lindelöf and converging ω₁-sequences

• Autorzy: Alan Dow , Klaas Pieter Hart
• Języki publikacji: EN

Abstrakty

EN

We deal with a conjectured dichotomy for compact Hausdorff spaces: each such space contains a non-trivial converging ω-sequence or a non-trivial converging ω₁-sequence. We establish that this dichotomy holds in a variety of models; these include the Cohen models, the random real models and any model obtained from a model of CH by an iteration of property K posets. In fact in these models every compact Hausdorff space without non-trivial converging ω₁-sequences is first-countable and, in addition, has many ℵ₁-sized Lindelöf subspaces. As a corollary we find that in these models all compact Hausdorff spaces with a small diagonal are metrizable.

Kategorie tematyczne

• 54D30: Compactness
• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54A35: Consistency and independence results
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 224
• Numer: 3
• Strony: 205-218

Daty

wydano

2014

Twórcy

autor

Alan Dow

• Department of Mathematics, UNC-Charlotte, 9201 University City Blvd., Charlotte, NC 28223-0001, U.S.A.

autor

Klaas Pieter Hart

• Faculty of Electrical Engineering, Mathematics, and Computer Science, TU Delft, Postbus 5031, 2600 GA Delft, the Netherlands

Identyfikatory

DOI

10.4064/fm224-3-1