Continuity properties of probabilistic norms (Q1359585)

A. N. Serstnev introduced the notion of probabilistic spaces which was recently modified by \textit{C. Alsina}, \textit{B. Schweizer} and \textit{A. Sklar} [Aequationes Math. 46, No. 1-2, 91-98 (1993; Zbl 0792.46062)]. In this interesting paper, the authors investigate questions of continuity in probabilistic normed spaces. It is proved that vector addition is continuous with respect to the norm-induced topology where as multiplication by a fixed scalar can be discontinuous.