On characterization of locally $L^0$-convex topologies induced by a family of $L^0$-seminorms

Abstract

The purpose of this paper is to provide a characterization of the topological $L^0$-modules whose topology is induced by a family of $L^0$-seminorms using the gauge function for $L^0$-modules. Taking advantage of these ideas we will give a counterexample of a locally $L^0$-convex module whose topology is not induced by a family of $L^0$-seminorms.

Cited by in corpus (1)

• A counterexample shows that not every locally $L^0$--convex topology is necessarily induced by a family of $L^0$--seminorms