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arXiv · 2303.10205

Local structure of homogeneous $ANR$-spaces

Vesko Valov
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Abstract

We investigate to what extend finite-dimensional homogeneous locally compact $ANR$-spaces have common properties with Euclidean manifolds. Specially, the local structure of homogeneous $ANR$-spaces is described. Using that description, we provide a positive solution of the problem whether every finite-dimensional homogeneous metric $ANR$-compactum $X$ is dimensionally full-valued, i.e. $\dim X\times Y=\dim X+\dim Y$ for any metric compactum $Y$.

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Vesko Valov. 2023-03-17. Local structure of homogeneous $ANR$-spaces. https://arxiv.org/abs/2303.10205

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