Abstract
In this paper we investigate the cohomological dimension of cohomologically locally connected compacta with respect to principal ideal domains. We show the cohomological dimension version of the Borsuk-Siecklucki theorem: for every uncountable family {Kα}αεA of n-dimensional closed subsets of an n-dimensional ANR-compactum, there exist α ≠ β such that dim(Kα ∩ Kβ) = n. As its consequences we shall investigate the equality of cohomological dimension and strong cohomological dimension and give a characterization of cohomological dimension by using a special base. Furthermore, we shall discuss the relation between cohomological dimension and dimension of cohomologically locally connected spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 39-50 |
| Number of pages | 12 |
| Journal | Topology and its Applications |
| Volume | 113 |
| Issue number | 1-3 |
| Publication status | Published - 2001 Dec 1 |
Keywords
- ANR
- Cohomological dimension
- Cohomology locally n-connected
- Principal ideal domain
ASJC Scopus subject areas
- Geometry and Topology
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Dydak, J., & Koyama, A. (2001). Cohomological dimension of locally connected compacta. Topology and its Applications, 113(1-3), 39-50.