We introduce the concept of Baire embeddings and we classify them up to C conjugacies. We show that two such embeddings are Cequivalent if and only if they have exponentially equivalent geometries. Next, we introduce the class of IFS-like Baire embeddings and we also show that two Hölder equivalent IFS-like Baire embeddings are C conjugate if and only if their scaling functions are the same. In...

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

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 ...

Perhaps the earliest results about pointwise compact sets of Baire class-1 functions are the two selection theorems of E. Helly found in most of the standard texts on real variable (see, e.g., [Lo], [N]). These two theorems are really theorems about a particular example of a compact set of Baire class-1 functions known today as Helly space, the space of all nondecreasing functions from the unit...

Calude, C., Relativized topological size of sets of partial recursive functions (Note), Theoretical Computer Science 87 (1991) 347-352. In [ 11, a recursive topology on the set of unary partial recursive functions was introduced and recursive variants of Baire topological notions of nowhere dense and meagre sets were defined. These tools were used to measure the size of some classes of partial ...