- Tytuł:
- Approximable dimension and acyclic resolutions
- Autorzy:
-
Koyama, A.
Sher, R. - Powiązania:
- https://bibliotekanauki.pl/articles/1205457.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
approximable dimension
cohomological dimension
acyclic resolution
$UV^{n-1}$-resolution
universal space
refinable mapping - Opis:
- We establish the following characterization of the approximable dimension of the metric space X with respect to the commutative ring R with identity: $a-dim_R$ X ≤ n if and only if there exist a metric space Z of dimension at most n and a proper $UV^{n-1}$-mapping f:Z → X such that $\check H^n(f^-1}(x);R) = 0 $ for all x ∈ X. As an application we obtain some fundamental results about the approximable dimension of metric spaces with respect to a commutative ring with identity, such as the subset theorem and the existence of a universal space. We also show that approximable dimension (with arbitrary coefficient group) is preserved under refinable mappings.
- Źródło:
-
Fundamenta Mathematicae; 1997, 152, 1; 43-53
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł