Porosity and \(\sigma\)-porosity. (English) Zbl 0666.26003

The notion of porous set has been introduced by E. P. Dolzhenko in 1967. One can find similar notions already in some papers by Denjoy and Khintchine. The theory and application of porous, sigma-porous and generalized porous sets has been developed by numerous mathematicians, among them the main rule was played by the present author. It turns out that porous sets appear very frequently in studies of cluster sets and in differentiation theory. The paper under review presents state of art at 1987. The list of references includes 94 positions.
Reviewer: W.Wilczyński


26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A03 Foundations: limits and generalizations, elementary topology of the line
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26B05 Continuity and differentiation questions
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets