Some examples on quasi-barrelled spaces

Manuel Valdivia

Annales de l'institut Fourier (1972)

  • Volume: 22, Issue: 2, page 21-26
  • ISSN: 0373-0956

Abstract

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The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled 𝒟 ℱ -space containing a subspace of infinite countable codimension which is not 𝒟 ℱ -space, and bornological barrelled space which is not inductive limit of Baire space.

How to cite

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Valdivia, Manuel. "Some examples on quasi-barrelled spaces." Annales de l'institut Fourier 22.2 (1972): 21-26. <http://eudml.org/doc/74077>.

@article{Valdivia1972,
abstract = {The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled $\{\cal D\}\{\cal F\}$-space containing a subspace of infinite countable codimension which is not $\{\cal D\}\{\cal F\}$ -space, and bornological barrelled space which is not inductive limit of Baire space.},
author = {Valdivia, Manuel},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {21-26},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some examples on quasi-barrelled spaces},
url = {http://eudml.org/doc/74077},
volume = {22},
year = {1972},
}

TY - JOUR
AU - Valdivia, Manuel
TI - Some examples on quasi-barrelled spaces
JO - Annales de l'institut Fourier
PY - 1972
PB - Association des Annales de l'Institut Fourier
VL - 22
IS - 2
SP - 21
EP - 26
AB - The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled ${\cal D}{\cal F}$-space containing a subspace of infinite countable codimension which is not ${\cal D}{\cal F}$ -space, and bornological barrelled space which is not inductive limit of Baire space.
LA - eng
UR - http://eudml.org/doc/74077
ER -

References

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  1. [1] N. BOURBAKI, Éléments de Mathématiques, Livre V : Espaces vectoriels topologiques, (ch. III, ch. IV, ch. V), Paris (1964). 
  2. [2] J. DIEUDONNÉ, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math., 25, 50-55 (1952). Zbl0049.08202MR15,38b
  3. [3] A. GROTHENDIECK, Sur les espaces (F) et (DF), Summa Brasil. Math., 3, 57-123 (1954). Zbl0058.09803MR17,765b
  4. [4] A. GROTHENDIECK, Produits tensoriels topologiques et espaces nucléaires Mem. Math. Soc., 16 (1955). Zbl0064.35501MR17,763c
  5. [5] G. KOTHE, Topological Vector Spaces I, Berlin-Heidelberg-New York, Springer (1969). Zbl0179.17001MR40 #1750
  6. [6] M. VALDIVIA, A hereditary property in locally convex spaces, Ann. Inst. Fourier, 21, 1-2 (1971). Zbl0205.40903MR48 #11967
  7. [7] M. VALDIVIA, On final topologies, J. Reine angew. Math., 251, 193-199 (1971). Zbl0223.46003MR45 #4108
  8. [8] M. VALDIVIA, On D F spaces, Math. Ann., 191, 38-43 (1971). Zbl0204.12802MR43 #6694
  9. [9] M. VALDIVIA, A class of bornological barrelled spaces which are not ultrabornological, Math. Ann. 194, 43-51 (1971). Zbl0207.42701MR47 #2307
  10. [10] M. VALDIVIA, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier, 21, 3-13 (1971). Zbl0205.40904MR48 #11968

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