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For subsets of $\mathbb{R}^+$ we consider the local right upper porosity andthe local right lower porosity as elements of a cluster set of all porositynumbers. 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 porositynumbers of a set, features of the scaling functions and the geometry ofso-called pretangent spaces to this set.

Local one-side porosity and pretangent spaces