2006/09/04 by István Juhász, Istvan Juhasz, Juhasz, Istvan +5
Computer Science · Mathematics · #54A25 (Secondary) #54A35 (Primary) 03E35 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #math.GN #math.LO #msc:03E35 #msc:54A25 #msc:54A35
paper · pdf · doi:10.48550/arxiv.math/0609092
arxiv created 2006/09/04 · openalex publication_date 2006/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A space X is said to be κ-resolvable (resp. almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (resp. almost disjoint over the ideal of nowhere dense subsets). X is maximally resolvable iff it is Δ(X)-resolvable, where Δ(X) = min\|G| : G ≠ ∅ open\. We show that every crowded monotonically normal (in short: MN) space is ω-resolvable and almost μ-resolvable, where μ= min\2ω, ω2 \. On the other hand, if κ is a measurable cardinal then there is a MN space X with Δ(X) = κ such that no subspace of X is ω1-resolvable. Any MN space of cardinality < ℵω is maximally resolvable. But from a supercompact cardinal we obtain the consistency of the existence of a MN space X with |X| = Δ(X) = ℵω such that no subspace of X is ω2-resolvable.