Strong Cohomological Dimension

Volume 56 / 2008

Jerzy Dydak, Akira Koyama Bulletin Polish Acad. Sci. Math. 56 (2008), 183-189 MSC: 55M10, 54F45. DOI: 10.4064/ba56-2-9

Abstract

We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that $\mathop{\rm Ind}_G X = \dim_G X$ if $X$ is a separable metric ANR and $G$ is a countable Abelian group. Hence $\dim_{\mathbb{Z}} X = \dim X$ for any separable metric ANR $X$.

Authors

  • Jerzy DydakDepartment of Mathematics
    University of Tennessee
    Knoxville, TN 37996, U.S.A.
    e-mail
  • Akira KoyamaDepartment of Mathematics
    Faculty of Sciences
    Shizuoka University
    Oya 836, Shizuoka 422-8529, Japan
    e-mail

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