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Theory of Computing Systems

, Volume 62, Issue 5, pp 1109–1124 | Cite as

Co-c.e. Sets with Disconnected Complements

  • Zvonko Iljazović
  • Bojan Pažek
Article

Abstract

We examine co-c.e. sets with disconnected complements in a computable metric space. We focus on the case when the computable metric space is effectively locally connected and when the connected components of the complement of a co-c.e. set S can be effectively distinguished. We give a sufficient condition that such an S contains a computable point and a sufficient condition that S is computable.

Keywords

Computable metric space Co-c.e. set Computable point Effective local connectedness 

Notes

Acknowledgements

The authors would like to thank the anonymous referee for his useful suggestions.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  2. 2.Faculty of ArchitectureUniversity of ZagrebZagrebCroatia

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