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.

29 pages

References in corpus (3)

• Tangent spaces to metric spaces and to their subspaces
• Metric spaces with unique pretangent spaces
• Uniform boundedness of pretangent spaces, local constancy of metric derivatives and strong right upper porosity at a point