Co-c.e. Sets with Disconnected Complements
- 41 Downloads
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.
- 4.Miller, J.S.: Effectiveness for embedded spheres and balls, Electronic notes in theoretical computer science, volume 66, Elsevier, 127–138 (2002)Google Scholar
- 9.Iljazović, Z., Pažek, B.: Computable intersection points, preprintGoogle Scholar
- 14.Specker, E.: Der Satz vom maximum in der rekursiven analysis. In: Heyting, A. (ed.) Constructivity in Mathematics, pp. 254–265. North Holland Publica. Comp., Amsterdam (1959)Google Scholar