2010/03/12 by Lajos Soukup, Soukup, Lajos
Computer Science · Mathematics · #03E35 #54A25 #54A35 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1003.2496
openalex publication_date 2010/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that it is consistent that the continuum is as large as you wish, and for each uncountable cardinal κ below the continuum, there are a subset T of the reals and a family A of countable subsets of T such that (1) both T and A have cardinality κ, (2) |a∩ T|=κ for each a∈ A, (3) for each uncountable subset of T contains some elements of A, and so (i) there is an almost disjoint family of subsets of the reals with size and chromatic number κ, (ii) there is a locally compact, locally countable T2 space with cardinality spectrum \ω,κ\.