
Journal of Lie Theory 18 (2008), No. 4, 915917 Copyright Heldermann Verlag 2008 A Counterexample in the Dimension Theory of Homogeneous Spaces of Locally Compact Groups Adel A. George Michael Mathematics and Sciences Unit, Dhofar University, P.O. Box 2509, 211 Salalah, Sultanate of Oman adelgeorge1@yahoo.com [Abstractpdf] We construct a locally compact group $G$ and a closed subgroup $H$ such that such that the quotient space $G/H$ is connected and has weight $w(G/H)=2^{\aleph_0}$ but fails to contain a cube $\I^{w(G/H)}$ of the same weight. This proves as incorrect an assertion made in Theorem 4.2 of K. H. Hofmann and S. A. Morris: Transitive actions of compact groups and topological dimension, J. of Algebra {\boldface 234} (2000), 454479. Keywords: Homogeneous spaces of locally compact groups, Tychonoff cube, dimension. MSC: 22D05 [ Fulltextpdf (115 KB)] for subscribers only. 