Absolutely convex sets in barrelled spaces

Manuel Valdivia

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 2, page 3-13
  • ISSN: 0373-0956

Abstract

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If { A n } is an increasing sequence of absolutely convex sets, in a barrelled space E , such that ⋃ n = 1 ∞ A n = E , it is deduced some properties of E from the properties of the sets of { A n } . It is shown that in a barrelled space any subspace of infinite countable codimension, is barrelled.

How to cite

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Valdivia, Manuel. "Absolutely convex sets in barrelled spaces." Annales de l'institut Fourier 21.2 (1971): 3-13. <http://eudml.org/doc/74038>.

@article{Valdivia1971,
abstract = {If $\lbrace A_n\rbrace $ is an increasing sequence of absolutely convex sets, in a barrelled space $E$, such that $ \bigcup ^\infty _\{n=1\} A_n = E$, it is deduced some properties of $E$ from the properties of the sets of $\lbrace A_n\rbrace $. It is shown that in a barrelled space any subspace of infinite countable codimension, is barrelled.},
author = {Valdivia, Manuel},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {3-13},
publisher = {Association des Annales de l'Institut Fourier},
title = {Absolutely convex sets in barrelled spaces},
url = {http://eudml.org/doc/74038},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Valdivia, Manuel
TI - Absolutely convex sets in barrelled spaces
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 2
SP - 3
EP - 13
AB - If $\lbrace A_n\rbrace $ is an increasing sequence of absolutely convex sets, in a barrelled space $E$, such that $ \bigcup ^\infty _{n=1} A_n = E$, it is deduced some properties of $E$ from the properties of the sets of $\lbrace A_n\rbrace $. It is shown that in a barrelled space any subspace of infinite countable codimension, is barrelled.
LA - eng
UR - http://eudml.org/doc/74038
ER -

References

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  1. [1] I. AMEMIYA und Y. KOMURA, Uber nicht-vollständige Montelräume. Math. Annalen. 177, 273-277, (1968). Zbl0157.43903MR38 #508
  2. [2] M. DE WILDE, Sur les sous-espaces de codimension finie d'un espace linéaire à semi-normes, To appear in Bull. Soc. R. Sciences, Liége. Zbl0187.37201
  3. [3] J. DIEUDONNÉ, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Pol. Math. 25, 50-55, (1952). Zbl0049.08202MR15,38b
  4. [4] J. HORVÁTH, Topological Vector Spaces and Distributions. I. Massachussets (1966). Zbl0143.15101MR34 #4863
  5. [5] G. KÖTHE, Die Bilräume abgeschlossener Operatoren, J. für die reine und And. Math., 232, 110-111, (1968). Zbl0157.21003

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