Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.

In this paper we introduce Peano path derivatives as a natural extension of the notion of path derivatives. We give a sufficient condition on a system of paths to ensure the corresponding Peano path derivative is Baire 1. As consequences, we obtain that unilateral approximate and unilateral Iapproximate Peano derivatives are Baire one. In studying generalized derivatives, one of the first quest...

In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...

We investigate the connectedness and Baire classification of a function associated with the statistical limit superior.

Given a cardinal κ, a set A ⊂ ω is κ-universally Baire if there exist trees S, T which project to A and its complement respectively, and which continue to project to complements after the forcing Coll(ω, κ). Todorcevic [3] has shown that under Martin’s Maximum every set of reals of cardinality א1 is א1-universally Baire but not א2-universally Baire. Here we present alternate proofs of these two...

We extend Baire results about nα-sequences in different ways, in particular we investigate sequences with multidimensional indices.

In the article concepts and facts necessary to continue forma-lization of theory of continuous lattices according to [10] are introduced. The notation and terminology used here are introduced in the following papers: