Abstract: Using the theories of topological systems and Quantale, we first introduced the concept of subsystem of Quantale system to define the embedding between Quantale systems, and then with the help of the structure of Quantale, the embedding theorem of Quantale system was obtained. The embedding theorem was used to study the embedding of spatilization of Quantale system. It was proved that all subsystems of a Quantale system were complete lattices under the defined partial orders.

Key words: subsystem, Quantale system, embedding, complete lattice