2009/11/14 by Márton Elekes, Elekes, Márton, Tamás Mátrai +3 · 1 citation
Computer Science · Mathematics · #03C25 #03E04 #03E05 #03E15 #03E35 #03E40 #03E50 #03E65 #05C15 #06A05 #52A20 #52B11 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.0911.2774
openalex publication_date 2009/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a set, \ka be a cardinal number and let \iH be a family of subsets of X which covers each x∈ X at least \ka times. What assumptions can ensure that \iH can be decomposed into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover \iH: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly ordered sets and covers of \realn by polyhedra and by arbitrary convex sets. We focus on these problems mainly for infinite κ. Besides numerous positive and negative results, many questions turn out to be independent of the usual axioms of set theory.