Abstract. We prove that the lattice $\mathop{\rm Eq} \Omega $ of all equivalence relations on an infinite set $\Omega $ contains, as a $0,1$-sublattice, the $0$-coproduct of two copies of itself, thus answering a question by G. M. Bergman. Hence, by using methods initiated by de Bruijn and further developed by Bergman, we obtain that $\mathop{\rm Eq} \Omega $ also contains, as a sublattice, the coproduct of $2^{\mathop{\rm card}\Omega }$ copies of itself.

AMS Subject Classification (1991): 06B15; 06B10, 06B25

Keyword(s): Lattice, equivalence relation, embedding, coproduct, ideal, filter, upper continuous

Received October 1, 2007. (Registered under 6444/2009.)