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

Name: On characterization of locally $L^0$-convex topologies induced by a family of $L^0$-seminorms
Creator: Garc��a, Jos�� Miguel Zapata
Keywords: FOS: Mathematics, Functional Analysis (math.FA)

Garc��a, Jos�� Miguel Zapata

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https://dx.doi.org/10.48550/ar...

Article . 2014

License: arXiv Non-Exclusive Distribution

Data sources: Datacite

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

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2014Embargo end date: 01 Jan 2014Publisher:arXiv

Authors: Garc��a, Jos�� Miguel Zapata;

doi: 10.48550/arxiv.1404.0357

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

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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.

Keywords

FOS: Mathematics, Functional Analysis (math.FA)

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