ABSTRACT
This chapter discusses several results and statements closely connected with Sierpinski’s partition of the Euclidean plane. It shows that there is a beautiful equivalent of Continuum Hypothesis in terms of differentiability of real-valued functions. The chapter also provides that the existence of a well-ordering of the real line R immediately yields the existence of subsets of R having a very bad descriptive structure from the points of view of the Lebesgue measurability and Baire property.
