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- W870865308 abstract "We introduce and investigate the notion of (strong) K n G -manifolds, where G is an abelian group. One of the result related to that notion (Theorem 3.4) implies the following partial answer to the Bing-Borsuk problem (5), whether any partition of a homogeneous metric ANR-space X of dimension n is cyclic in dimension n − 1: If X is a homogeneous metric ANR compactum with y H n (X;G) 6 0, then y H n 1 (M;G) 6 0 for every set M ⊂ X, which is cutting X between two disjoint open subsets of X. Another implication of Theorem 3.4 (Corollary 3.6) provides an analog of the classical result of Mazurkiewicz (24) that no region in R n can be cut by a subset of dimension ≤ n − 2. Concerning homology manifolds, it is shown that if X is arcwise connected complete metric space which is either a homology n-manifold over a group G or a product of at least n metric spaces, then X is a Mazurkiewicz arc n-manifold. We also introduce a property which guarantees that Hk(X,Xx;G) = 0 for every x ∈ X and k ≤ n−1, where X is a homogeneous locally compact metric ANR." @default.
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- W870865308 date "2013-01-13" @default.
- W870865308 modified "2023-09-27" @default.
- W870865308 title "ALEXANDROFF TYPE MANIFOLDS AND HOMOLOGY MANIFOLDS" @default.
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