Tensor products in the category of topological vector spaces are not associative

2003/07/03 by Helge Glockner, Glockner, Helge
Mathematics · #22A05 #46A16 #46A32 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:22A05 #msc:46A16 #msc:46A32

paper · pdf · doi:10.48550/arxiv.math/0307041

7 pages; v2: new version focusses on the real case

arxiv created 2004/04/30 · arxiv updated 2009/11/30

Abstract

We show by example that the associative law does not hold for tensor products in the category of general (not necessarily locally convex) topological vector spaces. The same pathology occurs for tensor products of Hausdorff abelian topological groups.

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