ABSTRACT
This chapter is devoted to the so-called Luzin subsets of the real line R and to the Sierpinski subsets of R. These sets are useful in various questions of real analysis and measure theory. Also, they have a number of applications in modern set theory and in certain topics of general topology. The chapter emphasizes the fact that the existence of Luzin and Sierpinski subsets of R cannot be established within ZFC theory. Luzin sets possess a number of specific features important from the point of view of their applications in real analysis and topology. The chapter point outs some similarities between Luzin and Sierpinski sets. It also uses Martin’s Axiom for giving a construction of a generalized Sierpinski set with the Baire property.
