Rice’s Theorem in Effectively Enumerable Topological Spaces

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9136)

Abstract

In the framework of effectively enumerable topological spaces, we investigate the following question: given an effectively enumerable topological space whether there exists a computable numbering of all its computable elements. We present a natural sufficient condition on the family of basic neighborhoods of computable elements that guarantees the existence of a principal computable numbering. We show that weakly-effective \(\omega \)–continuous domains and the natural numbers with the discrete topology satisfy this condition. We prove weak and strong analogues of Rice’s theorem for computable elements.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.A.P. Ershov Institute of Informatics SystemsSbRASNovosibirskRussia
  2. 2.Sobolev Institute of MathematicsSbRASNovosibirskRussia

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