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, 35:247--260, 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.


  BACK
Back to overview of papers


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 = "247-260" }