Tangent spaces to general metric spaces (Q2891112)

Let \((X,d)\) be a metric space, \(a\in X\) be some point, and \(n\geq 2\) be a natural number. Then, \({\text{card}}[\Omega(a,\bar r)]\leq n\) holds for every pretangent space \(\Omega(a,\bar r)\), if and only if \(F_n(x_1,...,x_n)\to 0\) as \(x_1\to a\), ..., \(x_n\to a\). (Here, \(F_n:X^n\to \mathbb R\) is a function defined in terms of \((d(x_i,x_j); 1\leq i,j\leq n)\) and \((d(x_k,a); 1\leq k\leq n)\)).