  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.
