2015/11/02 by Ігор Протасов, Protasov, Igor
Computer Science · Mathematics · #22A05 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1511.01046
openalex publication_date 2015/11/02 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We say that a topological group G is partially box κ-resolvable if there exist a dense subset B of G and a subset A of G, |A|=κ such that the subsets \ aB: a∈ A\ are pairwise disjoint. If G=AB then G is called box κ-resolvable. We prove two theorems. If a topological group G contains an injective convergent sequence then G is box ω-resolvable. Every infinite totally bounded topological group G is partially box n-resolvable for each natural number n, and G is box κ-resolvable for each infinite cardinal κ, κ