On the structure of the space of continuous maps with zero topological entropy
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.
In this paper we prove that each differentiation basis associated with a -adic path system defined by a bounded sequence satisfies the Ward Theorem.
The -finiteness of a variational measure, generated by a real valued function, is proved whenever it is -finite on all Borel sets that are negligible with respect to a -finite variational measure generated by a continuous function.
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.
We investigate the topological structure of the space 𝓓ℬ₁ of bounded Darboux Baire 1 functions on [0,1] with the metric of uniform convergence and with the p*-topology. We also investigate some properties of the set Δ of bounded derivatives.
In this paper a full totalization is presented of the Kurzweil-Henstock integral in the multidimensional space. A residual function of the total Kurzweil-Henstock primitive is defined.