On splitting infinite-fold covers

• Autorzy: Márton Elekes , Tamás Mátrai , Lajos Soukup
• Języki publikacji: EN

Abstrakty

EN

Let X be a set, κ be a cardinal number and let ℋ be a family of subsets of X which covers each x ∈ X at least κ-fold. What assumptions can ensure that ℋ can be decomposed into κ many disjoint subcovers?
We examine this problem under various assumptions on the set X and on the cover ℋ: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly ordered sets and covers of ℝⁿ by polyhedra and by arbitrary convex sets. We focus on problems with κ infinite. Besides numerous positive and negative results, many questions turn out to be independent of the usual axioms of set theory.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 03E04: Ordered sets and their cofinalities; pcf theory
• 05C15: Coloring of graphs and hypergraphs
• 03E40: Other aspects of forcing and Boolean-valued models
• 03E05: Other combinatorial set theory
• 03E65: Other hypotheses and axioms
• 03E15: Descriptive set theory
• 03C25: Model-theoretic forcing
• 52B11: n -dimensional polytopes
• 52A20: Convex sets in n dimensions (including convex hypersurfaces)
• 06A05: Total order
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 212
• Numer: 2
• Strony: 95-127

Daty

wydano

2011

Twórcy

autor

Márton Elekes

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary

autor

Tamás Mátrai

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary

autor

Lajos Soukup

• Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary

Identyfikatory

DOI

10.4064/fm212-2-1