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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67963We 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.7 pages; v2: new version focusses on the real caseFunctional Analysis46A16, 46A32, 22A05Tensor products in the category of topological vector spaces are not associativetext