Valdivia, Manuel The space of distributions \(D'(\Omega)\) is not \(B_r\)-complete. (English) Zbl 0288.46033 Math. Ann. 211, 145-149 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 10 Documents MSC: 46F05 Topological linear spaces of test functions, distributions and ultradistributions 46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness) × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Dieudonné, J., Schwartz, L.: La dualité dans les espaces (F) et (DF). Ann. Inst. Fourier1, 61-101 (1950) [2] Grothendieck, A.: Product tensoriels topologiques et espaces nucléaires. Mem. Amer Math. Soc. No.16 (1965) [3] Grothendieck, A.: Sur les espaces (F) et (DF). Summa Brasil. Math.3, 57-123 (1954) · Zbl 0058.09803 [4] Köthe, G.: Topological vector spaces. I. Berlin-Hamburg-New York: Springer 1969 · Zbl 0179.17001 [5] Ptâk, V.: Completeness and the open mapping theorem. Bull. Soc. Math. France86, 41-74 (1958) · Zbl 0082.32502 [6] Schwartz, L.: Sur le théorème du graphe fermé. C. R. Acad. Sc. Paris263, Serie A, 602-605 (1966) · Zbl 0151.19202 [7] Smoljanov, O. G.: The spaceD is not hereditarily complete. Izv. Akad. Nauk SSSR, Ser. Math. Tom35 (3), 686-696 (1971); Math. USSR Izvestija5 (3), (1971) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.