Pombo, D. P. jun. Completion of spaces of homogeneous polynomials. (English) Zbl 0639.46007 C. R. Acad. Bulg. Sci. 40, No. 11, 19-21 (1987). The main result of this article is a representation of the completion of certain topological vector spaces of continuous m-homogeneous polynomials, extending previous theorems of A. Grothendieck, A. P. and W. Robertson, N. Adasch and N. Adasch, B. Ernst and D. Keim. Since we deal with (polynomial) mappings between topological vector spaces over a nontrivially valued field of characteristic zero, the above mentioned result can be applied in the Archimedean and non-Archimedean contexts (as indicated in the text). Reviewer: D.P.Pombo Cited in 1 Document MSC: 46A32 Spaces of linear operators; topological tensor products; approximation properties 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis 46E40 Spaces of vector- and operator-valued functions Keywords:representation of the completion of certain topological vector spaces of continuous m-homogeneous polynomials; non-Archimedean contexts PDFBibTeX XMLCite \textit{D. P. Pombo jun.}, C. R. Acad. Bulg. Sci. 40, No. 11, 19--21 (1987; Zbl 0639.46007)