The concept of homogeneous integrity constraints in database systems is introduced. The metric space for the state of database schemes with homogeneous integrity constraints is established. It is shown that many common integrity constraints that are used in practice satisfy the condition of homogeneity of integrity constraints. Such constraints include key, referential, joint, and many-to-many integrity constraints, etc. The proposed constructs allow one to design metric spaces for the state of database schemes and enable the study of integrity constraints of databases based on the methods and concepts of "continuous mathematics."