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1. MAXIMAL CLASSES FOR THE FAMILY OF [λ ᵘ]-CONTINUOUS FUNCTIONS.

Author

Kowalczyk, Stanisław and Nowakowska, Katarzyna

Subjects
*MATHEMATICAL functions, *SET theory, *MATHEMATICAL analysis, *DIFFERENTIAL equations, *MATHEMATICS
Abstract

In this paper we give the definition of [λ ᵘ]-continuity of real-valued functions defined on an open interval, which is an example of path continuity. We give some properties of [λ, ᵘ]-continuous functions. The aim of the paper is to find the maximal additive class and the maximal multiplicative class for the family of [λ, ᵘ]-continuous functions. [ABSTRACT FROM AUTHOR]

Published
2011

2. ON CAUCHY TYPE CHARACTERIZATIONS OF CONTINUITY AND BAIRE ONE FUNCTIONS.

Author

Jachymski, Jacek, Lindner, Monika, and Lindner, Sebastian

Subjects
*MATHEMATICAL functions, *CAUCHY integrals, *TOPOLOGY, *DIFFERENTIAL equations, *MATHEMATICAL analysis, *MATHEMATICS
Abstract

In the paper of Lee et al. an equivalent condition for a function ƒ to be of the first Baire class has been established. This condition is of an ε -- δ type, similarly as in Cauchy's definition of continuity of a function. In the first part of this paper we examine a problem whether it is possible to obtain other classes of functions by further modifications of the above condition. It turns out that, in some sense, the answer is negative. In the second part we consider a topological version of the condition of Lee et al. [ABSTRACT FROM AUTHOR]

Published
2004