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arXiv · 1404.0357

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

José Miguel Zapata García
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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.

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José Miguel Zapata García. 2014-04-29. On characterization of locally $L^0$-convex topologies induced by a family of $L^0$-seminorms. https://arxiv.org/abs/1404.0357

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