An introduction to shell porosity (Q1308826)

The author has defined the new notion of shell porosity in a similar way as the classical notion of porosity [see \textit{L. Zajíček}, Acta Univ. Carol., Math. Phys. 28, No. 1, 57-61 (1987; Zbl 0666.26002)] using the differences of two concentric balls instead of balls disjoint with the set. This notion is equivalent to symmetric porosity on the real line. The aim of the paper is to compare the class of sigma shell porous sets with other classes of sets (hyperporous, totally porous, etc.) and to study basic properties of shell porous sets. Among others it is proved that a typical compact set in a complete space is strongly shell porous, a closed sigma shell porous set in a complete space is totally disconnected and that the product of two shell porous sets having sufficiently big shell porosity is again shell porous.