Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
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
Czasopismo
Rocznik
Tom
Numer
Strony
205-218
Opis fizyczny
Daty
wydano
2014
Twórcy
autor
- Department of Mathematics, UNC-Charlotte, 9201 University City Blvd., Charlotte, NC 28223-0001, U.S.A.
autor
- Faculty of Electrical Engineering, Mathematics, and Computer Science, TU Delft, Postbus 5031, 2600 GA Delft, the Netherlands
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-3-1