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 |
| Externally published | Yes |
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Keywords
- ANR
- Cohomological dimension
- Cohomology locally n-connected
- Principal ideal domain
ASJC Scopus subject areas
- Geometry and Topology
Cite this
Cohomological dimension of locally connected compacta. / Dydak, Jerzy; Koyama, Akira.
In: Topology and its Applications, Vol. 113, No. 1-3, 2001, p. 39-50.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Cohomological dimension of locally connected compacta
AU - Dydak, Jerzy
AU - Koyama, Akira
PY - 2001
Y1 - 2001
N2 - 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.
AB - 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.
KW - ANR
KW - Cohomological dimension
KW - Cohomology locally n-connected
KW - Principal ideal domain
UR - http://www.scopus.com/inward/record.url?scp=0002871207&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0002871207&partnerID=8YFLogxK
M3 - Article
VL - 113
SP - 39
EP - 50
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
IS - 1-3
ER -