Archive for Mathematical Logic

, Volume 46, Issue 7–8, pp 679–693 | Cite as

On degree-preserving homeomorphisms between trees in computable topology

  • Iraj Kalantari
  • Larry Welch


In this paper we first give a variant of a theorem of Jockusch–Lewis– Remmel on existence of a computable, degree-preserving homeomorphism between a bounded strong \({\Pi^0_2}\) class and a bounded \({\Pi^0_1}\) class in 2 ω . Namely, we show that for mathematically common and interesting topological spaces, such as computably presented \({\mathbb{R}^n}\) , we can obtain a similar result where the homeomorphism is in fact the identity mapping. Second, we apply this finding to give a new, priority-free proof of existence of a tree of shadow points computable in 0′.


Computability theory Recursion theory Topology \({\Pi_1^0}\) Trees Recursive analysis Computable analysis Recursive topology Computable topology Avoidable points Shadow points 

Mathematical Subject Classification (2000)

03D45 03D80 03C57 54A20 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsWestern Illinois UniversityMacombUSA

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