Translation-invariant generalized topologies induced by probabilistic norms
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One considers probabilistic normed spaces as defined by Alsina,Schweizer and Sklar, but with non necessarily continuous triangle functions. Such spaces are endowed with a generalized topology that is Fréchet-separated, translation-invariant and countably generated by radial and circled 0-neighborhoods. Conversely, we show that such generalized topologies are probabilistically normable.
Probabilistic Normed Spaces