Computable Invariance

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 suucient condition for non-computability, but a discontinuous function might still be computably invariant. We investigate algebraic conditions which guarantee that a discon-tinuous function is suuciently discontinuous and suuciently eeective such that it is not computably invariant. Our main theorem generalizes the First Main Theorem ouf Pour-El & Richards (cf. 20]). We apply our theorem to prove that several set-valued operators are not computably invariant.