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On the entropy of Darboux functions

Ryszard J. Pawlak (2009)

Colloquium Mathematicae

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 insertion of Darboux functions

Aleksander Maliszewski (1998)

Fundamenta Mathematicae

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 pointwise limits of sequences of Świątkowski functions

Tomasz Natkaniec, Julia Wódka (2018)

Czechoslovak Mathematical Journal

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 uniform limit of quasi-continuous functions.

Baltasar Rodríguez-Salinas (2001)

RACSAM

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.

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