On Dranishnikov's cell-like resolution

Akira Koyama, Katsuya Yokoi

Research output: Contribution to journalArticle

Abstract

We prove the following theorem: Theorem 1. For a compactum X with c-dimℤ/p X ≤ n and c-dimℤ(q) X ≤ n for some distinct prime numbers p, q, and c-dim X ≤ n + 1, where n > 1, there exists an (n + 1)-dimensional compactum Z with c-dimℤ/p Z ≤ n, c-dimℤ(q) Z ≤ n and a cell-like map f : Z → X. Moreover, giving the following theorem, we note that Theorem 1 cannot be true in the case of n = 1. Theorem 2. For every pair p, q of distinct prime numbers there exists an infinite-dimensional compactum X such that c-dimℤ/p X = 1, c-dimℤ(q), X = 1 and c-dim X = 2.

Original languageEnglish
Pages (from-to)87-106
Number of pages20
JournalTopology and its Applications
Volume113
Issue number1-3
Publication statusPublished - 2001 Dec 1
Externally publishedYes

Keywords

  • Cell-like resolution
  • Cohomological dimension
  • Edwards-Walsh resolution

ASJC Scopus subject areas

  • Geometry and Topology

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