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- W2963967352 abstract "Let $X$ be a Hausdorff topological group and $G$ a locally compact subgroup of $X$. We show that $X$ admits a locally finite $sigma$-discrete $G$-functionally open cover each member of which is $G$-homeomorphic to a twisted product $Gtimes_H S_i$, where $H$ is a compact large subgroup of $G$ (i.e., the quotient $G/H$ is a manifold). If, in addition, the space of connected components of $G$ is compact and $X$ is normal, then $X$ itself is $G$-homeomorphic to a twisted product $Gtimes_KS$, where $K$ is a maximal compact subgroup of $G$. This implies that $X$ is $K$-homeomorphic to the product $G/Ktimes S$, and in particular, $X$ is homeomorphic to the product $Bbb R^ntimes S$, where $n={rm dim,} G/K$. Using these results we prove the inequality $ {rm dim}, Xle {rm dim}, X/G + {rm dim}, G$ for every Hausdorff topological group $X$ and a locally compact subgroup $G$ of $X$." @default.
- W2963967352 created "2019-07-30" @default.
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- W2963967352 date "2013-01-01" @default.
- W2963967352 modified "2023-09-26" @default.
- W2963967352 title "Locally compact subgroup actions on topological groups" @default.
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