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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2016 | 233 | 3 | 257-270

## Local cohomological properties of homogeneous ANR compacta

EN

### Abstrakty

EN
In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball 𝔹ⁿ ⊂ ℝⁿ and its boundary $𝕊^{n-1}$. We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that every 3-dimensional homogeneous metric ANR compactum is dimensionally full-valued.

257-270

wydano
2016

### Twórcy

autor
• Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada