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A+ CATEGORY SCIENTIFIC UNIT

Borsuk's quasi-equivalence is not transitive

Volume 197 / 2007

Andrzej Kadlof, Nikola Koceić Bilan, Nikica Uglešić Fundamenta Mathematicae 197 (2007), 215-227 MSC: Primary 54C99; Secondary 55P55. DOI: 10.4064/fm197-0-9

Abstract

Borsuk's quasi-equivalence relation on the class of all compacta is considered. The open problem concerning transitivity of this relation is solved in the negative. Namely, three continua , Y and Z lying in \mathbb{R}^{3} are constructed such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.

Authors

  • Andrzej KadlofWarsaw University, Poland
    e-mail
  • Nikola Koceić BilanDepartment of Mathematics
    University of Split
    Teslina 12/III
    21000 Split, Croatia
    e-mail
  • Nikica UglešićDepartment of Mathematics
    University of Split
    Teslina 12/III
    21000 Split, Croatia
    e-mail

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