On nonbornological barrelled spaces

Manuel Valdivia

Annales de l'institut Fourier (1972)

  • Volume: 22, Issue: 2, page 27-30
  • ISSN: 0373-0956

Abstract

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If E is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of E . The same result is obtained replacing “barrelled” by “quasi-barrelled”.

How to cite

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Valdivia, Manuel. "On nonbornological barrelled spaces." Annales de l'institut Fourier 22.2 (1972): 27-30. <http://eudml.org/doc/74079>.

@article{Valdivia1972,
abstract = {If $E$ is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of $E$. The same result is obtained replacing “barrelled” by “quasi-barrelled”.},
author = {Valdivia, Manuel},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {27-30},
publisher = {Association des Annales de l'Institut Fourier},
title = {On nonbornological barrelled spaces},
url = {http://eudml.org/doc/74079},
volume = {22},
year = {1972},
}

TY - JOUR
AU - Valdivia, Manuel
TI - On nonbornological barrelled spaces
JO - Annales de l'institut Fourier
PY - 1972
PB - Association des Annales de l'Institut Fourier
VL - 22
IS - 2
SP - 27
EP - 30
AB - If $E$ is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of $E$. The same result is obtained replacing “barrelled” by “quasi-barrelled”.
LA - eng
UR - http://eudml.org/doc/74079
ER -

References

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  1. [1] N. BOURBAKI, Sur certains spaces vectoriels topologiques, Ann. Inst. Fourier, 5-16 (1950). Zbl0042.35302MR13,137d
  2. [2] J. DIEUDONNÉ, Recent development in the theory of locally convex spaces, Bull. Amer. Math. Soc., 59, 495-512 (1953). Zbl0053.25701MR15,963a
  3. [3] J. DIEUDONNÉ, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math., 25, 50-55 (1952). Zbl0049.08202MR15,38b
  4. [4] Y. KOMURA, Some examples on linear topological spaces, Math. Ann., 153, 150-162 (1964). Zbl0149.33604MR32 #2884
  5. [5] L. NACHBIN, Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci., USA, 40, 471-474 (1954). Zbl0055.09803MR16,156h
  6. [6] T. SHIROTA, On locally convex vector spaces of continuous functions, Proc. Jap. Acad., 30, 294-298 (1954). Zbl0057.33801MR16,275d

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