Local structure of homogeneous $ANR$-spacesThe results in the present paper show that the homogeneous locally compact
$ANR$-spaces share many properties of Euclidean spaces.
This is in accordance with the Bing-Borsuk conjecture \cite{bb} stating that
every $n$-dimensional homogeneous metric $ANR$-compactum with $n\geq 3$ is an
Euclidean manifold.
We describe the local structure of homogeneous $ANR$-spaces. 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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