Nikola Koceić Bilan*
University of Split, Croatia
Borsuk's quasi-equivalence is not transitive
We consider the Borsuk relation of quasi-equivalence on the class of all compacta, and solve, in the negative, the open problem (posed by Borsuk in 1976) concerning transitivity of the quasi-equivalence. Namely, we construct three continua X, Y and Z lying in R3 such that X is quasi-equivalent to Y and Y is quasi-equivalent to Z, while X is not quasi-equivalent to Z.
* This is a joint work with Andrzey Kadlof and Nikica Uglešić.
