Complementation problems for the Baire classes
William G. Bade · Pacific Journal of Mathematics · 1973
This paper initiates a study of the classes of Baire measurable functions on the unit interval I from the standpoint of the theory of spaces of continuous functions.For each countable ordinal a, the αth Baire class 3B« has a representation as C(Ω a ), where Ω a is a certain compactification of the discrete set I. For 1 S a Ω a induced by the imbedding of 53« in 23β, and consists of showing that this map admits no "averaging operator."It depends heavily on recent results in the theory of averaging operators due to S. Z. Ditor.In this paper scalars and functions are real valued.However, the arguments extend easily to the complex case.In the last section we show how corresponding results may be obtained when / is replaced by any uncountable compact metric space.