On the number of separable locally convex spaces
HTML articles powered by AMS MathViewer
- by Lech Drewnowski and Robert H. Lohman PDF
- Proc. Amer. Math. Soc. 58 (1976), 185-188 Request permission
Abstract:
The number of distinct separable locally convex spaces is shown to be ${2^{{2^c}}}$. The number of distinct separable and complete, or metrizable, or normed locally convex spaces is shown to be ${2^c}$. There is no separable locally convex space that is quotient-universal for the class of separable locally convex spaces.References
-
S. Banach, Théorie des opérations linéaires, Mongrafie Mat., PWN, Warsaw, 1932; reprint, Chelsea, New York, 1955. MR 17, 175.
S. Banach and S. Mazur, Zur Theorie der linearen Dimension, Studia Math. 4 (1933), 100-112.
- Joseph Diestel and Robert H. Lohman, Applications of mapping theorems to Schwartz spaces and projections, Michigan Math. J. 20 (1973), 39–44. MR 316993
- J. Dieudonné, Sur les propriétés de permanence de certains espaces vectoriels topologiques, Ann. Soc. Polon. Math. 25 (1952), 50–55 (1953) (French). MR 0056189
- R. Engelking, Outline of general topology, North-Holland Publishing Co., Amsterdam; PWN—Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. Translated from the Polish by K. Sieklucki. MR 0230273
- Seymour Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0200692
- Robert H. Lohman, An embedding theorem for separable locally convex spaces, Canad. Math. Bull. 14 (1971), 114–120. MR 291756, DOI 10.4153/CMB-1971-023-1
- Robert H. Lohman and Wilbur J. Stiles, On separability in linear topological spaces, Proc. Amer. Math. Soc. 42 (1974), 236–237. MR 326350, DOI 10.1090/S0002-9939-1974-0326350-X
- S. Mazur and W. Orlicz, Sur les espaces métriques linéaires. II, Studia Math. 13 (1953), 137–179 (French). MR 68730, DOI 10.4064/sm-13-2-137-179
- E. S. Pondiczery, Power problems in abstract spaces, Duke Math. J. 11 (1944), 835–837. MR 11104
- Stefan Rolewicz, Metric linear spaces, Monografie Matematyczne, Tom 56. [Mathematical Monographs, Vol. 56], PWN—Polish Scientific Publishers, Warsaw, 1972. MR 0438074
- 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
- Manuel Valdivia, On weak compactness, Studia Math. 49 (1973), 35–40. MR 333644, DOI 10.4064/sm-49-1-35-40
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 185-188
- MSC: Primary 46A05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417728-6
- MathSciNet review: 0417728