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Pereira Pombo, Dinamérico jun.

A note on polynomially barreled locally convex spaces. (English) Zbl 0538.46003

Ann. Fac. Sci. Toulouse, V. Sér., Math. 5, 281-286 (1983).
See the preview in Zbl 0525.46003.

MSC:

46A08 Barrelled spaces, bornological spaces

Keywords:

vector-valued continuous polynomials; sequentially complete polynomially infrabarreled locally convex spaces are polynomially barreled

Citations:

Zbl 0525.46003
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\textit{D. Pereira Pombo jun.}, Ann. Fac. Sci. Toulouse, Math. (5) 5, 281--286 (1983; Zbl 0538.46003)
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References:

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[2] J.A. Barroso , M.C. Matos , L. Nachbin . On holomorphy versus linearity in classifying locally convex spaces . In Infinite dimensional holomorphy and applications (Editor : M.C. Matos), North-Holland Publishing Company ( 1977 ), 31 - 74 . MR 473817 | Zbl 0399.46034 · Zbl 0399.46034
[3] N. Bourbaki . Espaces vectoriels topologiques . Hermann . · Zbl 0042.35302
[4] A. Grothendieck . Sur les espaces F et DF . Summa Brasiliensis Mathematicae 3 ( 1954 ), 57 - 123 . MR 75542 | Zbl 0058.09803 · Zbl 0058.09803
[5] K. Kothe . Topological vector spaces II . Springer-Verlag . Zbl 0417.46001 · Zbl 0417.46001
[6] L. Nachbin . Topology on spaces of holomorphic mappings . Ergebnisse der Mathematik 47 ( 1969 ), Springer-Verlag . MR 254579 | Zbl 0172.39902 · Zbl 0172.39902
[7] L. Nachbin . Some holomorphically significant properties of locally convex spaces . In Functional Analysis (Editor : D. de Figueiredo), Marcel Dekker ( 1976 ), 251 - 277 . MR 632068 | Zbl 0344.46100 · Zbl 0344.46100
[8] D.P. Pombo Jr . On polynomial classification of locally convex spaces . Studia Mathematica , accepted for publication. · Zbl 0495.46002
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