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.
