Semiéquicontinuité approximative et measurabilité
Semigroups of ...-density continuous functions.
Separating sets by Darboux-like functions
We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).
Sharkovskiĭ's theorem holds for some discontinuous functions
We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected graph.
Slowly oscillating continuity.
Some characterizations of pointwise discontinuous functions
Some Characterizations of the Darboux Continuity of Real Functions
Some generalizations of the notion of continuity and Denjoy property of functions
Some mean value theorems as consequences of the Darboux property
The aim of the paper is to present some mean value theorems obtained as consequences of the intermediate value property. First, we will prove that any nonextremum value of a Darboux function can be represented as an arithmetic, geometric or harmonic mean of some different values of this function. Then, we will present some extensions of the Cauchy or Lagrange Theorem in classical or integral form. Also, we include similar results involving divided differences. The paper was motivated by some problems...
Some regularity properties of algorithms and additive functions with respect to them.
Some results on projection of planar sets
In this paper we define certain types of projections of planar sets and study some properties of such projections.
Some results on (-pre, )-continuous functions.
Strong convergence and Dini theorems for non-uniform spaces
Sul modulo di continuità alla frontiera della soluzione del problema di Dirichlet relativo ad una classe di operatori parabolici
Sums and limits of almost continuous functions
Sums of Darboux and continuous functions
It is shown that for every Darboux function F there is a non-constant continuous function f such that F + f is still Darboux. It is shown to be consistent - the model used is iterated Sacks forcing - that for every Darboux function F there is a nowhere constant continuous function f such that F + f is still Darboux. This answers questions raised in [5] where it is shown that in various models of set theory there are universally bad Darboux functions, Darboux functions whose sum with any nowhere...
Sur la quasi-continuité et la quasi-continuité approximative
Sur le maximum approximatif
Sur les fonctions approximativement continues
Sur les fonctions discontinues croissantes et sur certaines fonctions continues