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 $X$, $Y$
 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~$Z$.

1. Warsaw University, Poland
   
2. Department of Mathematics
   University of Split
   Teslina 12/III
   21000 Split, Croatia
   
3. Department of Mathematics
   University of Split
   Teslina 12/III
   21000 Split, Croatia