K-Trivial Closed Sets and Continuous Functions

Authors:
George Barmpalias;Douglas Cenzer;Jeffrey B. Remmel;Rebecca Weber
Affiliations:
School of Mathematics, University of Leeds, Leeds LS2 9JT, England;Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida 32611,;Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112,;Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551,
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

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Abstract

We investigate the notion of K-triviality for closed sets and continuous functions. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial $\Pi^0_1$ class with no computable elements. For any K-trivial degree d, there is a K-trivial continuous function of degree d.