Computability
Complexity theory of real functions
Complexity theory of real functions
Computability on computable metric spaces
Theoretical Computer Science
Computable analysis: an introduction
Computable analysis: an introduction
Topological properties of real number representations
Theoretical Computer Science
Effective metric spaces and representations of the reals
Theoretical Computer Science
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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 infinitary basic functions of the structures are necessary.