The universality of the hyperpolar images of the Sierpinski carpet and the Menger sponge

Continuing with the development of a theory of hyperpolar fractals, we present in this article a way of constructing hyperpolar universal sets in two and three dimensions which are mappings of two classical fractals: the Sierpinski carpet and the Menger sponge. This article is, therefore, a continuation of a previous one (Glaser, 1996) and its aim is to extend some of the results of the Polish mathematician Waclaw Sierpinski (1882-1969) as well as some of the work of his Austrian colleague, Karl Menger (born in 1902) into two and three-dimensional hyperpolar spaces respectively.