Significance We extend the concept of metals and dielectrics to the “generalized metal/dielectric” by treating a pure metal or dielectric as the limiting case of a metal–dielectric layered metamaterial. Specifically, the metamaterial with metal filling ratio larger than one-half shares the same topological invariant as a pure metal and thus exhibits some metallic behaviors. In contrast, the dielectric-rich metamaterial and a pure dielectric are topologically equivalent and display dielectric properties. The topological edge state exists between the generalized metal and dielectric, giving the surface plasmon polariton (SPP) an additional physical meaning: the limiting case of a topological edge state.