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 infinitary basic functions of the structures are necessary.
Acknowledgement
I would like to thank an anonymous referee for some useful hints.
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Hemmerling, A. (2001). Standard Representations of Effective Metric Spaces. In: Blanck, J., Brattka, V., Hertling, P. (eds) Computability and Complexity in Analysis. CCA 2000. Lecture Notes in Computer Science, vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45335-0_4
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DOI: https://doi.org/10.1007/3-540-45335-0_4
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