Abstract. We prove the following result of the second and third authors: Any ho-where G is a principal ideal domain. This implies that any homogeneous n-dimensional metric ANR-continuum is a V n -continuum in the sense of Alexandroff.We also prove that any finite-dimensional homogeneous metric continuum X, satisfyingȞ n (X; G) = 0 for some group G and n ≥ 1, cannot be separated by a compactum K withȞ n−1 (K; G) = 0 and dim G K ≤ n − 1. This provides a partial answer to a question of Kallipoliti-Papasoglu whether any two-dimensional homogeneous Peano continuum cannot be separated by arcs.
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