Journal of Lie Theory

no. 4
A Counterexample in the Dimension Theory of Homogeneous Spaces of Locally Compact Groups
Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 915-917
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), 454--479.
DOI: 10.5802/jolt.532
Classification: 22D05
Keywords: Homogeneous spaces of locally compact groups, Tychonoff cube, dimension 
@article{JOLT_2008_18_4_a9,
     author = {A. A. George Michael},
     title = {A {Counterexample} in the {Dimension} {Theory} of {Homogeneous} {Spaces} of {Locally} {Compact} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {915--917},
     year = {2008},
     volume = {18},
     number = {4},
     doi = {10.5802/jolt.532},
     zbl = {1160.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.532/}
}
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A. A. George Michael. A Counterexample in the Dimension Theory of Homogeneous Spaces of Locally Compact Groups. Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 915-917. doi: 10.5802/jolt.532

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