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Decomposing Borel functions using the Shore-Slaman join theorem
[article]
2013
arXiv
pre-print
Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each F_σ set under it is again F_σ. Many researchers conjectured that the Jayne-Rogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-Slaman join theorem on the Turing degrees, we show the following variant of the Jayne-Rogers theorem at
arXiv:1304.0698v1
fatcat:khw75v6g2vglpnc2f6g5u5hnaq