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Journal of Convex Analysis 24 (2017), No. 2, 383--391
Copyright Heldermann Verlag 2017

On the Characterization of Locally L0-Convex Topologies Induced by a Family of L0-Seminorms

José M. Zapata
Dpto. Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain

The purpose of this paper is to provide a characterization of locally L0-convex modules induced by a family of L0-seminorms using the gauge function for L0-modules and discussing the notion of countable concatenation. Taking advantage of these ideas we will give a counterexample of a locally L0-convex topology not induced by any family of L0-seminorms.

Keywords: L0-modules, locally L0-convex modules, gauge function, countable concatenation, countable concatenation closure.

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