Continuous functions need not have \(\sigma\)-porous graphs. (English) Zbl 0607.26005

Foran, James

Real Anal. Exch. 11(1985/86), 194-203 (1986).

The author gives an example of a continuous function \(f:[0,1]\to R\) whose graph is a non-\(\sigma\)-porous subset of the plane and has the Hausdorff dimension 2.

Reviewer: J.S.Lipiński

MSC:

26A15	Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
28A05	Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28A75	Length, area, volume, other geometric measure theory

Keywords:

\(\sigma \)-porous graphs; continuous functions; non-\(\sigma \)-porous subset