Some continuous maps on the space of clones in multiple-valued logic

The lattice L_k of all clones over the set {0, 1,···, k-1} is known to be a metric space. In this paper, we define some maps induced by the lattice operators and note that those induced by the meet operator are continuous maps from L_k to L_k. Secondly, we use the meet operator to construct two continuous maps from L₃ to L₂. These maps are shown to be order-preserving and surjective. Finally, the images of all the maximal clones in L₃ and those of Yanov-Muchnik clones in L₃ under these maps are studied