Dovgoshey, Oleksiy; Martio, Olli Tangent spaces to general metric spaces. (English) Zbl 1265.54117 Rev. Roum. Math. Pures Appl. 56, No. 2, 137-155 (2011). 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 \((d(x_k,a); 1\leq k\leq n)\)). Reviewer: Mihai Turinici (Iasi) Cited in 1 ReviewCited in 11 Documents MSC: 54E35 Metric spaces, metrizability 54C30 Real-valued functions in general topology Keywords:tangent space; finite; complete PDFBibTeX XMLCite \textit{O. Dovgoshey} and \textit{O. Martio}, Rev. Roum. Math. Pures Appl. 56, No. 2, 137--155 (2011; Zbl 1265.54117)