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

The lattice L/sub k/ of all clones over the set {0, 1,/spl middot//spl middot//spl middot/, 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/sub k/ to L/sub k/. Secondly, we use the meet operator to construct two continuous maps from L/sub 3/ to L/sub 2/. These maps are shown to be order-preserving and surjective. Finally, the images of all the maximal clones in L/sub 3/ and those of Yanov-Muchnik clones in L/sub 3/ under these maps are studied.