Computable invariance

  • Vasco Brattka
Session 5: Computability
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1276)


In Computable Analysis each computable function is continuous and computably invariant, i.e. it maps computable points to computable points. On the other hand, discontinuity is a sufficient condition for non-computability, but a discontinuous function might still be computably invariant. We investigate algebraic conditions which guarantee that a discontinuous function is sufficiently discontinuous and sufficiently effective such that it is not computably invariant. Our main theorem generalizes the First Main Theorem ouf Pour-El and Richards (cf. [18]). We apply our theorem to prove that several set-valued operators are not computably invariant.


Banach Space Computable Point Unbounded Operator Discontinuous Function Recursion Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Vasco Brattka
    • 1
  1. 1.Theoretische Informatik IFern Universität HagenHagenGermany

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