Abstract

The purpose of this paper is to provide a characterization of locally L0L^0-convex modules induced by a family of L0L^0-seminorms using the gauge function for L0L^0-modules and discussing the notion of countable concatenation. Taking advantage of these ideas we will give a counterexample of a locally L0L^0-convex topology not induced by any family of L0L^0-seminorms.

Author information

Contact details are reproduced from the original publication and may be historical.

José M. Zapata

Dpto. Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain

jmzg1@um.es

Keywords

  • L0-modules
  • locally L0-convex modules
  • gauge function
  • countable concatenation
  • countable concatenation closure

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Suggested citation

J. M. Zapata. “On the Characterization of Locally L^0-Convex Topologies Induced by a Family of L^0-Seminorms.” Journal of Convex Analysis 24 (2017), No. 2, 383–391. https://doi.org/10.68381/jca24026

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.