On the topologies induced by a cone

2014/03/27 by Mehdi Ghasemi, Ghasemi, Mehdi
Engineering · Mathematics · #28C05 #28E99 #47A57 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Mathematics and Applications #math.FA #msc:28C05 #msc:28E99 #msc:47A57

paper · pdf · doi:10.48550/arxiv.1403.6913

arxiv created 2014/03/27 · openalex publication_date 2014/03/27 · arxiv updated 2014/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a commutative and unital ℝ-algebra, and M be an Archimedean quadratic module of A. We define a submultiplicative seminorm ‖⋅‖_M on A, associated with M. We show that the closure of M with respect to ‖⋅‖_M-topology is equal to the closure of M with respect to the finest locally convex topology on A. We also compute the closure of any cone in ‖⋅‖_M-topology. Then we omit the Archimedean condition and show that there still exists a lmc topology associated to M, pursuing the same properties.

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