TY - JOUR
T1 - Cohomological dimension of locally connected compacta
AU - Dydak, Jerzy
AU - Koyama, Akira
N1 - Funding Information:
* Corresponding author. This paper was started when the first author visited Osaka Kyoiku University. Supported in part by grant DMS-9704372 from the National Science Foundation. E-mail addresses: dydak@math.utk.edu (J. Dydak), koyama@cc.osaka-kyoiku.ac.jp (A. Koyama).
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
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
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U2 - 10.1016/s0166-8641(00)00018-3
DO - 10.1016/s0166-8641(00)00018-3
M3 - Article
AN - SCOPUS:0002871207
VL - 113
SP - 39
EP - 50
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
IS - 1-3
ER -