On families of Lindelöf and related subspaces of $2^{ω₁}$

• Autorzy: Lúcia Junqueira , Piotr Koszmider
• Języki publikacji: EN

Abstrakty

EN

We consider the families of all subspaces of size ω₁ of $2^{ω₁}$ (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in $[X]^{ω₁}$ are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used is forcing and in this case various preservation or nonpreservation results of topological and combinatorial properties are proved. In particular we prove that there may be no c.c.c. forcing which destroys the Lindelöf property of compact spaces, answering a question of Juhász. Many related questions are formulated.

Kategorie tematyczne

• 03E55: Large cardinals
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54A35: Consistency and independence results
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 169
• Numer: 3
• Strony: 205-231

Daty

wydano

2001

Twórcy

autor

Lúcia Junqueira

• Departamento de Matemática, Universidade de Säo Paulo, Caixa Postal 66281, Säo Paulo, SP, CEP: 05315-970, Brasil

autor

Piotr Koszmider

• Departamento de Matemática, Universidade de Säo Paulo, Caixa Postal 66281, Säo Paulo, SP, CEP: 05315-970, Brasil.

Identyfikatory

DOI

10.4064/fm169-3-2