2022/12/04 by Тарас Банах, Banakh, Taras
Mathematics · #03E50 #20E06 #22015 #22A05 #54H11 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2212.01750
openalex publication_date 2022/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For every infinite cardinal κ with κ+=2κ we construct a group G of cardinality |G|=κ+ such that (i) G is 36-Shelah, which means that A36=G for any subset A⊆ G of cardinality |A|=|G|; (ii) G is absolutely \mathsfT 1S-closed and projectively \mathsfT 1S-discrete, which means that for every homomorphism h:G→ Y to a T1 topological semigroup Y the image h[G] is a closed discrete subspace of Y, (iii) G cannot be covered by finitely many algebraic subsets, i.e., subsets of the form \x∈ G:xc1xc2⋯ xcn=e\ for some c1,c2,⋯,cn∈ G.