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Locally convex spaces with denumerable systems of weakly compact subsets

Published online by Cambridge University Press:  24 October 2008

D. J. H. Garling
D. J. H. Garling
Affiliation:
St John's College, Cambridge
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Extract

Let E be a locally convex vector space, and let (At) be a sequence of subsets of E, which cover E. Dieudonné (3) has proved the two following results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 813 - 815
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Bourbaki, N.Espaces vectoriels topologiques, Chapitres I–II (Paris, 1953).Google Scholar
(2)Bourbaki, N.Espaces vectoriels topologiques, Chapitres III–V (Paris, 1955).Google Scholar
(3)Dieudonné, J.Denumerability conditions in locally convex vector spaces. Proc. American Math. Soc. 8 (1957), 367–372.CrossRefGoogle Scholar
(4)Grothendieck, A.Sur les espaces (F) et (DF). Summa Brasil. Math. 3 (1954), 67–123.Google Scholar