Translation-invariant generalized topologies induced by probabilistic norms

Details Translation-invariant generalized topologies induced by probabilistic norms Translation-invariant generalized topologies induced by probabilistic norms

2005-05-23

arxiv.org/abs/math/0505484v2

Note di Matematica, Volume 29, Issue 1 (2009), 157-164

Mathematics

General Topology

8 pages. Some minor changes and corrections have been made

Scientific paper

10.1285/i15900932v29n1p157

In this paper we consider probabilistic normed spaces as defined by Alsina, Sklar, and Schweizer, but equipped with non necessarily continuous triangle functions. Such spaces endow a generalized topology that is Fr\'echet-separable, translation-invariant and countably generated by radial and circled 0-neighborhoods. Conversely, we show that such generalized topologies are probabilistically normable.

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