On the Characterization of Locally L
                    <sup>0</sup>
                    -Convex Topologies Induced by a Family of L
                    <sup>0</sup>
                    -Seminorms

DOI: 10.68381/jca24026 ISSN: 0944-6532

On the Characterization of Locally L ⁰ -Convex Topologies Induced by a Family of L ⁰ -Seminorms

José M. Zapata

The purpose of this paper is to provide a characterization of locally

L^0

L 0

-convex modules induced by a family of

L^0

L 0

-seminorms using the gauge function for

L^0

L 0

-modules and discussing the notion of countable concatenation. Taking advantage of these ideas we will give a counterexample of a locally

L^0

L 0

-convex topology not induced by any family of

L^0

L 0

-seminorms.