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Special subsets of the real line. (English) Zbl 0588.54035
Handbook of set-theoretic topology, 201-233 (1984).
[For the entire collection see Zbl 0546.00022.]
This is a survey paper concerning peculiar subsets of reals from the point of view of topology and measure theory. The following topics are covered: Luzin and Sierpinski sets, concentrated sets, sets of strong measure zero, sets of universal measure zero, \(\sigma\)-sets, Q-sets, C’ and C” sets, \(\lambda\) and \(\lambda\) ’-sets, perfectly meager sets. Some of the most important classical and recent results from this area are selected and presented. The choice is done in an excellent way proving the author’s deep knowledge of the subject.
Reviewer: A.Szymański

MSC:
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
54E52 Baire category, Baire spaces
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets