Translation-invariant generalized topologies induced by probabilistic norms

En One considers probabilistic normed spaces as defined by Alsina, Sklar, and Schweizer, but with non necessarily continuous triangle functions. Such spaces are endowed with a generalized opology that is Fr´echet-separated, translation-invariant and countably generated by radial and circled 0-neighborhoods. Conversely, we show that such generalized topologies are probabilistically normable