Borsuk's quasi-equivalence is not transitive

• Autorzy: Andrzej Kadlof , Nikola Koceić Bilan , Nikica Uglešić
• Języki publikacji: EN

Abstrakty

EN

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 ℝ³ 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.

Kategorie tematyczne

• 54C99: None of the above, but in this section
• 55P55: Shape theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 197
• Numer: 1
• Strony: 215-227

Daty

wydano

2007

Twórcy

autor

Andrzej Kadlof

• Warsaw University, Poland

autor

Nikola Koceić Bilan

• Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia

autor

Nikica Uglešić

• Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia

Identyfikatory

DOI

10.4064/fm197-0-9