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Abstrakty
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.
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.
Słowa kluczowe
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
Czasopismo
Rocznik
Tom
Numer
Strony
95-127
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
- Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
autor
- Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
autor
- Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-2-1