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The space of distributions \(D'(\Omega)\) is not \(B_r\)-complete. (English) Zbl 0288.46033


MSC:

46F05 Topological linear spaces of test functions, distributions and ultradistributions
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
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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)
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