Rice’s Theorem in Effectively Enumerable Topological Spaces

  • Margarita KorovinaEmail author
  • Oleg Kudinov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9136)


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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