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On countable locally convex direct sums. (English) Zbl 0312.46014

MSC:
46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
46A03 General theory of locally convex spaces
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References:
[1] J. Dieudonné, Sur les espaces de Montel métrizables. C. R. Acad. Sci. Paris238, 194-195 (1954). · Zbl 0055.09801
[2] G.Köthe, Topological Vector Spaces I. Berlin-Heidelberg-New York 1969. · Zbl 0179.17001
[3] V. Pták, Completeness and the open mapping theorem. Bull. Soc. Math. France86, 41-74 (1958). · Zbl 0082.32502
[4] M.Valdivia, OnB r -completeness. Ann. Inst. Fourier (Grenoble). (To appear.)
[5] M. Valdivia, Absolutely convex sets in barrelled spaces. Ann. Inst. Fourier (Grenoble)21, 3-13 (1971). · Zbl 0205.40904
[6] M.Valdivia, The space of distributionsD(?) is notB r -complete. Math. Ann. (To appear.)
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