Local one-side porosity and pretangent spaces

Abstract

For subsets of $\mathbb{R}^+$ we consider the local right upper porosity and the local right lower porosity as elements of a cluster set of all porosity numbers. The use of a scaling function $\mu:\mathbb{N} \to \mathbb{R}^+$ provides an extension of the concept of porosity numbers on subsets of $\mathbb{N}$. The main results describe interconnections between porosity numbers of a set, features of the scaling functions and the geometry of so-called pretangent spaces to this set.