Standard representations of effective metric spaces

Abstract

Representations of effective metric spaces which are equivalent to the normed Cauchy representations are called standard representations. They can be characterized by their computability properties, i.e., by having both computable extensions as well as inversions computable as relations. Another characterization is given by many-sorted so-called indicator functions. Under weak suppositions on the underlying spaces, there are also single-sorted effectively categorical structures characterizing the standard representations. To this purpose, both basic constants and in finitary basic functions of the structures are necessary.