Rudin-like sets and hereditary families of compact sets

• Autorzy: Étienne Matheron , Miroslav Zelený
• Języki publikacji: EN

Abstrakty

EN

We show that a comeager Π₁¹ hereditary family of compact sets must have a dense $G_δ$ subfamily which is also hereditary. Using this, we prove an "abstract" result which implies the existence of independent ℳ ₀-sets, the meagerness of 𝒰₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true $F_{σδ}$ sets.

Kategorie tematyczne

• 03E15: Descriptive set theory
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 185
• Numer: 2
• Strony: 97-116

Daty

wydano

2005

Twórcy

autor

Étienne Matheron

• Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France

autor

Miroslav Zelený

• Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75, Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/fm185-2-1