On the reflexivity symmetry and transitivity of the tangency relation of sets of the class \(\tilde M_{p,k}\) (Q1347009)

Let \(E_0\) consist of subsets of a set \(E\) and let \(l: E_0\times E_0\to \mathbb{R}_{\geq 0}\) (interpretation: distance function). Within this frame and with the help of two further real-valued functions \(k\)- tangency of sets \(A\), \(B\in E_0\) at a point \(p\in E\) is defined. The author states (for certain subsets of \(E_0\)) sufficient conditions such that \(k\)-tangency at \(p\) is an equivalence relation. The proofs contain some estimates which are only correct for limits.