On I-Asymmetry

Abstract

Sets of approximative asymmetry in the sense of category are introduced. The following theorem is proved. If $f : \mathbb{R}\to \mathbb{R}$ is a function, then the set of $\mathcal{I}$-asymmetry points of $f$ is of the type $F_{\sigma \delta \sigma}$ and is $\sigma$-well-porous. This illustrates the difference between measure and category. We give an example of a function with the set of $\mathcal{I}-$asymmetry points of the cardinality of the continuum.