Dense Subgroups of Prescribed Density

2025/07/17 by Peng, Dekui
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2507.13031

Abstract

Let G be an infinite compact group. We prove that for every cardinal κ between the density and the weight of G, there exists a dense subgroup of G of density κ.

Citations

• Locally Compact Groups with All Dense Subgroups Separable
• On the double density spectra of compact spaces
• The double density spectrum of a topological space
• Density character of subgroups of topological groups
• The weights of closed subgroups of a locally compact group

Related

• On density of infinite subsets I
• Finite groups with dense \cal CD-subgroups
• On density of infinite subsets II: dynamics on homogeneous spaces
• The weights of closed subgroups of a locally compact group
• Densities and Weights of Quotients of Precompact Abelian Groups