Another note on \(\sigma\)-porous sets (Q795946)

The authors introduce the notions of a globally porous set and a \(\sigma\)-globally porous set. They investigate these notions of global porousity and relate them to parental notions of porousity and uniform porousity. It is known [\textit{J. Foran} and \textit{P. D. Humke}, ibid. 6, 114-119 (1981; Zbl 0467.28001)] that there exists a \(\sigma\)-porous set which is contained in no \(\sigma\) porous \(F_{\sigma}\) set. Now the authors prove that a set is \(\sigma\)-globally porous if and only if it is contained in an \(F_{\sigma}\) set which is \(\sigma\)-globally porous. An example of a perfect porous set which is not \(\sigma\)-globally porous ends the paper. The definition of global porousity seems to be too long in order to be quoted in this review.