Let T be a T 0 non empty topological space and L 1 be a continuous sup-semilattice. Then Card the carrier of T Card the carrier of L 1 . Let T be a T 0 non empty topological space. Let T be a topological structure and L 1 be a continuous lower-bounded lattice. L 1 and T is finite.
Every finite lattice is arithmetic.
Let us note that every lattice which is finite is also arithmetic. Let us note that there exists a relational structure which is trivial, reflexive, transitive, antisymmetric, lower-bounded, non empty, finite, and strict and has l.u.b.'s and g.l.b.'s. Let L 1 be a finite lattice and B 1 be a CLbasis of L 1 with bottom. Let d be a set, p be a finite sequence, and i be a natural number. Suppose L 1 is infinite.