ON CANTOR-LIKE SETS AND CANTOR-LEBESGUE SINGULAR FUNCTIONS

ABSTRACT. In this paper we discuss several variations and generalizations of the Cantor set and study some of their properties. Also for each of those generalizations a Cantor-like function can be constructed from the set. We will discuss briefly the possible construction of those functions. 1. INTRODUCTION. The Cantor ternary set is the best example of a perfect nowhere-dense set in the real line. It was constructed by George Cantor in 1883, see [5], nevertheless it was not the first perfect nowhere-dense set in the real line to be constructed. The first construction was done by the a British mathematician Henry J. S. Smith in 1875, and Vito Volterra