Co-c.e. Sets with Disconnected Complements
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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.
KeywordsComputable metric space Co-c.e. set Computable point Effective local connectedness
The authors would like to thank the anonymous referee for his useful suggestions.
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