Abstract: The existence of some lattices and the lattice having the smallest set of generating elements are important in lattice theory.In this paper by means of the relations of the intrinsic topologies and admissible topology of a lattice,we prove there not exists the infinte complete and completely distributive lattice which has finite dimension.A complete boolean lattice Bpossesses the smallest set of generating elements iff B is completely distributive.

Key words:  , topological lattice, smallest set of generating elements, intrinsic topology