Bulletin of the American Mathematical Society

MathSciNet review: 1567234
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Book Information:

Authors: T. Husain and S. M. Khaleelulla
Title: Barrelledness in topological and ordered vector spaces
Additional book information: Lecture Notes in Math., vol. 692, Springer-Verlag, Berlin-Heidelberg-New York, 1978, x + 258 pp.

Nicolas Bourbaki, Sur certains espaces vectoriels topologiques, Ann. Inst. Fourier (Grenoble) 2 (1950), 5–16 (1951) (French). MR 42609

2.

M. DeWilde, Closed graph theorems and webbed spaces, Research Notes in Math., vol. 19, Pitman, London, San Francisco, Melbourne, 1978.

M. De Wilde and C. Houet, On increasing sequences of absolutely convex sets in locally convex spaces, Math. Ann. 192 (1971), 257–261. MR 288549, DOI 10.1007/BF02075355

J. Dieudonné, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math. 25 (1952), 50–55 (1953) (French). MR 0056189

Alexandre Grothendieck, Sur les espaces ($F$) et ($DF$), Summa Brasil. Math. 3 (1954), 57–123 (French). MR 75542

Taqdir Husain, Two new classes of locally convex spaces, Math. Ann. 166 (1966), 289–299. MR 212535, DOI 10.1007/BF01360784

S. O. Iyahen, On certain classes of linear topological spaces, Proc. London Math. Soc. (3) 18 (1968), 285–307. MR 226358, DOI 10.1112/plms/s3-18.2.285

Yukio K\B{o}mura, On linear topological spaces, Kumamoto J. Sci. Ser. A 5 (1962), 148–157 (1962). MR 151817

Mark Levin and Stephen Saxon, A note on the inheritance of properties of locally convex spaces by subspaces of countable codimension, Proc. Amer. Math. Soc. 29 (1971), 97–102. MR 280973, DOI 10.1090/S0002-9939-1971-0280973-2

M. Mahowald, Barrelled spaces and the closed graph theorem, J. London Math. Soc. 36 (1961), 108–110. MR 125426, DOI 10.1112/jlms/s1-36.1.108

Vlastimil Pták, Completeness and the open mapping theorem, Bull. Soc. Math. France 86 (1958), 41–74. MR 105606

Alex P. Robertson and Wendy Robertson, On the closed graph theorem, Proc. Glasgow Math. Assoc. 3 (1956), 9–12. MR 84108

Wendy Robertson, Completions of topological vector spaces, Proc. London Math. Soc. (3) 8 (1958), 242–257. MR 98298, DOI 10.1112/plms/s3-8.2.242

Stephen Saxon and Mark Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29 (1971), 91–96. MR 280972, DOI 10.1090/S0002-9939-1971-0280972-0

Manuel Valdivia, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier (Grenoble) 21 (1971), no. 2, 3–13 (English, with French summary). MR 333643

J. H. Webb, Sequential convergence in locally convex spaces, Proc. Cambridge Philos. Soc. 64 (1968), 341–364. MR 222602, DOI 10.1017/s0305004100042900

J. H. Webb, Countable-codimensional subspaces of locally convex spaces, Proc. Edinburgh Math. Soc. (2) 18 (1972/73), 167–172. MR 318824, DOI 10.1017/S0013091500009895

Yau-chuen Wong, Order-infrabarrelled Riesz spaces, Math. Ann. 183 (1969), 17–32. MR 253017, DOI 10.1007/BF01361260

Yau Chuen Wong and Kung Fu Ng, Partially ordered topological vector spaces, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1973. MR 0454581

1.

N. Bourbaki, Sur certains espaces vectoriels topologiques, Ann. Inst. Fourier (Grenoble) 2 (1950), 5-16. MR 0042609

2.

M. DeWilde, Closed graph theorems and webbed spaces, Research Notes in Math., vol. 19, Pitman, London, San Francisco, Melbourne, 1978.

3.

M. DeWilde and C. Houet, On increasing sequences of absolutely convex sets in locally convex spaces, Math. Ann. 192 (1971), 257-261. MR 288549

4.

J. Dieudonné, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math. 25 (1952), 50-55. MR 56189

5.

A. Grothendieck, Sur les espaces (F) et (D F), Summa Brasil. Math. 3 (1954), 57-123. MR 75542

6.

T. Husain, Two new classes of locally convex spaces, Math. Ann. 166 (1966), 289-299. MR 212535

7.

S. O. Iyahen, On certain classes of linear topological spaces, Proc. London Math. Soc. (3) 18 (1968), 285-307. MR 226358

8.

Y. Kōmura, On linear topological spaces, Kumamoto J. Sci. Ser. A 5 (1962), 148-157. MR 151817

9.

M. Levin and S. Saxon, A note on the inheritance of properties of locally convex spaces by subspaces of countable codimension, Proc. Amer. Math. Soc. 29 (1971), 97-102. MR 280973

10.

M. Mahowald, Barrelled spaces and the closed graph theorem, J. London Math. Soc. 36 (1961), 108-110. MR 125426

11.

V. Pták, Completeness and the open mapping theorem, Bull. Soc. Math. France 86 (1958), 41-74. MR 105606

12.

A. P. Robertson and W. J. Robertson, On the closed graph theorem, Proc. Glasgow Math. Assoc. 3 (1956), 9-12. MR 84108

13.

W. J. Robertson, Completions of topològical vector spaces, Proc. London Math. Soc. 8 (1958), 242-257. MR 98298

14.

S. Saxon and M. Levin, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29 (1971), 91-96. MR 280972

15.

M. Valdivia, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier (Grenoble) 21, (1971), fasc. 2, 3-13. MR 333643

16.

J. H. Webb, Sequential convergence in locally convex spaces, Proc. Cambridge Philos. Soc. 64 (1968), 341-364. MR 222602

17.

J. H. Webb, Countable-codimensional subspaces of locally convex spaces, Proc. Edinburgh Math. Soc. 18 (1972/73), 167-172. MR 318824

18.

Y.-C. Wong, Order-infrabarrelled Riesz spaces, Math. Ann. 183 (1969), 17-32. MR 253017

19.

Y.-C. Wong and K.-F. Ng, Partially ordered topological vector spaces, Oxford Math. Monograph, Clarendon Press, Oxford, 1973. MR 454581