PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 152 | 1 | 43-53
Tytuł artykułu

Approximable dimension and acyclic resolutions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
152
Numer
1
Strony
43-53
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-09-25
poprawiono
1996-08-16
Twórcy
autor
autor
  • Department of Mathematical Sciences, University of North Carolina at Greensboro, Greensboro, NC 27412, U.S.A., sherrb@iris.uncg.edu
Bibliografia
  • [1] A. N. Dranishnikov, Universal Menger compacta and universal mappings, Math. USSR-Sb. 57 (1987), 131-149.
  • [2] A. N. Dranishnikov, Homological dimension theory, Russian Math. Surveys 43 (4) (1988), 11-63.
  • [3] J. Dydak, The Whitehead and the Smale theorems in shape theory, Dissertationes Math. 156 (1979).
  • [4] J. Dydak and J. Mogilski, Universal cell-like maps, Proc. Amer. Math. Soc. 122 (1994), 943-948.
  • [5] R. Engelking, Dimension Theory, Math. Library 19, North-Holland, 1978.
  • [6] W. Hurewicz, Über dimensionserhöhende stetige Abbildungen, J. Reine Angew. Math. 169 (1933), 71-78.
  • [7] A. Koyama, Refinable maps in dimension theory, Topology Appl. 17 (1984), 247-255.
  • [8] A. Koyama, A characterization of compacta which admit acyclic $UV^{n-1}$-resolutions, Tsukuba J. Math. 20 (1996), 115-121.
  • [9] A. Koyama, Refinable maps in dimension theory II, Bull. Polish Acad. Sci. Math. 42 (1994), 255-261.
  • [10] A. Koyama and K. Yokoi, A unified approach of characterizations and resolutions for cohomological dimension modulo p, Tsukuba J. Math. 18 (1994), 247-282.
  • [11] W. Olszewski, Universal separable metrizable spaces of given cohomological dimension, Topology Appl. 61 (1995), 293-299.
  • [12] L. Rubin and P. Schapiro, Cell-like maps onto non-compact spaces of finite cohomological dimension, Topology Appl. 27 (1987), 221-244.
  • [13] J. Walsh, Dimension, cohomological dimension, and cell-like mappings, in: Lecture Notes in Math. 870, Springer, 1981, 105-118.
  • [14] K. Yokoi, Compactification and factorization theorems for transfinite covering dimension, Tsukuba J. Math. 15 (1991), 389-395.
  • [15] K. Yokoi, Cohomological dimension modulo p for metrizable spaces, Math. Japon., to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv152i1p43bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.