A Class of Connections between Systems of the Same Type Homomorphic Mapping and Isomorphic Mapping

The concept of systems of the same type is given, their homomorphic mapping and isomorphic mapping are introduced simultaneously, and the induced system of a given system is defined. Then the connection of homomorphism (isomorphism) between systems of the same type and their induced systems is proved by mapping function. In addition, homomorphism (isomorphism) invariant properties, total automorphism properties and category properties of systems of the same type are discussed, some applications are given.