Cohomological dimension of locally connected compacta

Jerzy Dydak; Akira Koyama

doi:10.1016/s0166-8641(00)00018-3

Cohomological dimension of locally connected compacta

Jerzy Dydak, Akira Koyama

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 {K_α}_αεA of n-dimensional closed subsets of an n-dimensional ANR-compactum, there exist α ≠ β such that dim(K_α ∩ K_β) = 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
DOIs	https://doi.org/10.1016/s0166-8641(00)00018-3
Publication status	Published - 2001
Externally published	Yes

Keywords

ANR
Cohomological dimension
Cohomology locally n-connected
Principal ideal domain

ASJC Scopus subject areas

Geometry and Topology

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10.1016/s0166-8641(00)00018-3

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title = "Cohomological dimension of locally connected compacta",

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.",

keywords = "ANR, Cohomological dimension, Cohomology locally n-connected, Principal ideal domain",

author = "Jerzy Dydak and Akira Koyama",

note = "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).",

year = "2001",

doi = "10.1016/s0166-8641(00)00018-3",

language = "English",

volume = "113",

pages = "39--50",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier",

number = "1-3",

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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).

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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DO - 10.1016/s0166-8641(00)00018-3

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JO - Topology and its Applications

JF - Topology and its Applications

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