Translation-invariant generalized topologies induced by probabilistic norms
General Topology
2010-08-09 v2 Probability
Abstract
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.
Cite
@article{arxiv.math/0505484,
title = {Translation-invariant generalized topologies induced by probabilistic norms},
author = {Bernardo Lafuerza-Guillen and Jose L. Rodriguez},
journal= {arXiv preprint arXiv:math/0505484},
year = {2010}
}
Comments
8 pages. Some minor changes and corrections have been made