Geodesic
On the Dimension of a Complete Metrizable Topological Vector Space
Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 271-272

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this note is to prove a result which is known to hold for Fréchet spaces [1, Chapitre II, §5, Exercise 24]. M. M. Day [2, p. 37] attributes the Banach space case to H. Löwig, although the earliest version that we have been able to find is that given by G. W. Mackey in [7, Theorem 1-1]. Recently H. E. Lacey has given an elegant proof for Banach spaces [5]. It is perhaps interesting to note that the non-locally convex case can be deduced from these known results which are established by duality arguments. 
Popoola, J. O.; Tweddle, I. On the Dimension of a Complete Metrizable Topological Vector Space. Canadian mathematical bulletin, Tome 20 (1977) no. 2, pp. 271-272. doi: 10.4153/CMB-1977-042-x
@article{10_4153_CMB_1977_042_x,
     author = {Popoola, J. O. and Tweddle, I.},
     title = {On the {Dimension} of a {Complete} {Metrizable} {Topological} {Vector} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {271--272},
     year = {1977},
     volume = {20},
     number = {2},
     doi = {10.4153/CMB-1977-042-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-042-x/}
}
TY  - JOUR
AU  - Popoola, J. O.
AU  - Tweddle, I.
TI  - On the Dimension of a Complete Metrizable Topological Vector Space
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 271
EP  - 272
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-042-x/
DO  - 10.4153/CMB-1977-042-x
ID  - 10_4153_CMB_1977_042_x
ER  - 
%0 Journal Article
%A Popoola, J. O.
%A Tweddle, I.
%T On the Dimension of a Complete Metrizable Topological Vector Space
%J Canadian mathematical bulletin
%D 1977
%P 271-272
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-042-x/
%R 10.4153/CMB-1977-042-x
%F 10_4153_CMB_1977_042_x

[1] 1. Bourbaki, N., Espaces Vectoriels Topologiques, Chapitres I et II, Hermann, Paris, 1966. Google Scholar

[2] 2. Day, M. M., Normed Linear Spaces, Springer-Verlag, Berlin, 1962. Google Scholar

[3] 3. Kelley, J. L., I. Namioka et al, Linear Topological Spaces, Van Nostrand, Princeton, 1963. Google Scholar

[4] 4. Köthe, G., Topological Vector Spaces I, Springer-Verlag, Berlin, 1969. Google Scholar

[5] 5. Lacey, H. E., The Hamel dimension of any infinite dimensional separable Banach space is c, Amer.Math. Monthly 80 (1973), 298. Google Scholar

[6] 6. Löwig, H., Über die Dimension linearer Räume, Studia Math. 5 (1935), 18-23. Google Scholar

[7] 7. Mackey, G. W., On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155-207. Google Scholar

Cité par Sources :