Sur la measurabilité des fonctions de plusieurs variables
Sur la structure de l'ensemble des points où une fonction continue n'admet pas de dérivée symétrique [Book]
Sur les classes de Baire des fonctions de deux variables
Sur les Classes de Baire des Fonctions Semi-Reelles
Sur les fonctions affines qui vérifient le calcul barycentrique
Sur les fonctions vectorielles approximativement continues
Sur les suites de fonctions approximativement continues et continues presque partout
Sur un problème concernant les fonctions quasicontinues
Sur une propriété des fonctions de deux variables
Symmetric porosity of symmetric Cantor sets
-equivalences generated by shape function on the real line
This paper is devoted to give a new method of generating T-equivalence using shape function and finding the exact calculation formulas of T-equivalence induced by shape function on the real line. Some illustrative examples are given.
The Borel structure of some non-Lebesgue sets
For a given function in some classes related to real derivatives, we examine the structure of the set of points which are not Lebesgue points. In particular, we prove that for a summable approximately continuous function, the non-Lebesgue set is a nowhere dense nullset of at most Borel class 4.
The coarsest topology for -approximately continuous functions
The Convex Hull of a Typical Compact Set.
The Henstock-Kurzweil approach to Young integrals with integrators in
In 1938, L. C. Young proved that the Moore-Pollard-Stieltjes integral exists if , and . In this note we use the Henstock-Kurzweil approach to handle the above integral defined by Young.
The Hurewicz covering property and slaloms in the Baire space
According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This...
The insertion of sets and fine topologies
The point of continuity property, neighbourhood assignments and filter convergences
We show that for some large classes of topological spaces X and any metric space (Z,d), the point of continuity property of any function f: X → (Z,d) is equivalent to the following condition: (*) For every ε > 0, there is a neighbourhood assignment of X such that d(f(x),f(y)) < ε whenever . We also give various descriptions of the filters ℱ on the integers ℕ for which (*) is satisfied by the ℱ-limit of any sequence of continuous functions from a topological space into a metric space.
The projective properties of the extreme path derivatives
Trajectories, first return limiting notions and rings of -connected and iteratively -connected functions
In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted ) contained between the families (widely described in literature) of Darboux Baire 1 functions () and connectivity functions (). The solutions to our problems are based, among other, on the suitable construction of the ring,...