Representation Theorem for Free Continuous Lattices

(2) Let L, S, T be complete non empty posets, f be a CLHomomorphism of L, S, and g be a CLHomomorphism of S, T . Then g · f is a CLHomomorphism of L, T . (3) For every non empty relational structure L holds idL is infs-preserving. (4) For every non empty relational structure L holds idL is directed-sups-preserving. (5) For every complete non empty poset L holds idL is a CLHomomorphism of L, L. (6) For every upper-bounded non empty poset L with g.l.b.’s holds 〈Filt(L),⊆〉 is a continuous subframe of 2the carrier of L ⊆ .