Borsuk's quasi-equivalence is not transitive

Tom 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

Streszczenie

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 $X$, $Y$ 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 $Z$.

Autorzy

  • 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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek