Cohomological dimension of locally connected compacta

Jerzy Dydak, Akira Koyama

Research output: Contribution to journalArticle

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 {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 languageEnglish
Pages (from-to)39-50
Number of pages12
JournalTopology and its Applications
Volume113
Issue number1-3
Publication statusPublished - 2001
Externally publishedYes

Fingerprint

Cohomological Dimension
Locally Connected
n-dimensional
Principal ideal domain
Compactum
Uncountable
Equality
Closed
Subset
Theorem

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 journalArticle

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