On the continuity for connected functions
On the convergence of -primitives
On the density maxima of a function
On the density of continuous functions in variable exponent Sobolev space.
On the differences of upper semicontinuous quasi-continuous functions
On the Durrmeyer-type modification of some discrete approximation operators.
On the entropy of Darboux functions
We prove some results concerning the entropy of Darboux (and almost continuous) functions. We first generalize some theorems valid for continuous functions, and then we study properties which are specific to Darboux functions. Finally, we give theorems on approximating almost continuous functions by functions with infinite entropy.
On the existence of -primitives on arbitrary metric spaces
On the family of functions with a closure of its graph of measure zero
On the insertion of Darboux functions
The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.
On the limits of sequences of Darboux a.e. quasi-continuous functions
On the maximum and the minimum of quasi-continuous functions
On the points of quasicontinuity and cliquishness of functions
On the pointwise limits of sequences of Świątkowski functions
The characterization of the pointwise limits of the sequences of Świątkowski functions is given. Modifications of Świątkowski property with respect to different topologies finer than the Euclidean topology are discussed.
On the prolongation of restrictions of Baire 1 functions to functions which are quasicontinuous and approximately continuous
Let I ⊂ ℝ be an open interval and let A ⊂ I be any set. Every Baire 1 function f: I → ℝ coincides on A with a function g: I → ℝ which is simultaneously approximately continuous and quasicontinuous if and only if the set A is nowhere dense and of Lebesgue measure zero.
On the set where an approximate derivative is a derivative
On the uniform limit of quasi-continuous functions.
Estudiamos cuando el límite uniforme de una red de funciones cuasi-continuas con valores en un espacio localmente convexo X es también una función cuasi-continua, resaltando que esta propiedad depende del menor cardinal de un sistema fundamental de entornos de O en X, y estableciendo condiciones necesarias y suficientes. El principal resultado de este trabajo es el Teorema 15, en el que los resultados de [7] y [10] son mejorados, en relación al Teorema de L. Schwartz.
On the -primitive
On theorems of Pu & Pu and Grande
Given a finite family of cliquish functions, , we can find a Lebesgue function such that is Darboux and quasi-continuous for every . This theorem is a generalization both of the theorem by H. W. Pu H. H. Pu and of the theorem by Z. Grande.
On uniform approximation of bounded approximately continuous functions by differences of lower semicontinuous and approximately continuous ones