Representations of the real numbers
and the open subsets of the set of real numbers. 

Klaus Weihrauch, Christoph Kreitz.  
Annals of pure and applied logic, 35:247260, 1987. 

Abstract 

In previous papers we have presented a unified Type 2 theory of computability
and continuity and a theory of representations. In this paper the concepts
developed so far are used for the foundation of a new kind of constructive
analysis. Different standard representations of the real numbers are
compared. It turns out that the crucial differences are of topological nature
and that most of the representations (e.g., the decimal representation) are
not reasonable for topological reasons. In the second part some effective
representations of the open subsets of the real numbers are introduced and
compared.

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Bibtex Entry 

@Article{ar:WeihrauchKreitz87a, author = "Klaus Weihrauch and Christoph Kreitz", title = "Representations of the real numbers and the open subsets of the set of real numbers", journal = "Annals of pure and applied logic", volume = 35, year = 1987, pages = "247260" } 