A classification of Baire-1 functions

Recursive Baire Classification and Speedable Functions

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not "small" whereas the set of infinitely often speedable functions is "large". In this way we offer partial answers to a question in [4]. MSC: 03D15.

On Some Properties of Baire-1 Functions

In this paper, we give alternative proofs of some of the properties of Baire-1 functions with respect to the new characterization of Baire-1 functions due to P.Y. Lee, W.K. Tang and D. Zhao. Some well-known functions were given to illustrate some of these properties. Mathematics Subject Classification: Primary 26A21

A New Characterization of Baire Class 1 Functions

We give a new characterization of the Baire class 1 functions (defined on an ultrametric space) by proving that they are exactly the pointwise limits of sequences of full functions, which are particularly simple Lipschitz functions. Moreover we highlight the link between the two classical stratifications of the Borel functions by showing that the Baire class functions of some level are exactly ...

2 Sequences of Baire Class 1 Functions 3

When are Borel functions Baire functions ?

The following two theorems give the flavour of what will be proved. THEOREM. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0, 1] to Y coincide if and only if Y is connected and locally connected. THEOREM. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class fun...