A metric characterization of the irrationals via a group operation (Q1074168)

A metric d for a topological space S is called a spyc metric if for each point x in S and each nonnegative real number r there exists a unique point y in S such that \(d(x,y)=r\). A space S is called a spyc space if it is separable and has a topology preserving spyc metric. Such a space is actually constructed in the plane. (1) There exist more than continuum- many nonhomeomorphic examples of spyc spaces. (2) Each complete spyc space is homeomorphic to the space of irrationals. An interesting matrix, called spyc, is defined. This matrix clarifies the subject.