Some order and topological properties of locally solid linear topological Riesz spaces
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- by C. D. Aliprantis PDF
- Proc. Amer. Math. Soc. 40 (1973), 443-447 Request permission
Abstract:
A theorem of Luxemburg and Zaanen on normed Riesz spaces (Theorem 2.4 below) and one of Nakano (Theorem 2.3 below) have been extended by the author in [1] to metrizable locally solid linear topological Riesz spaces. This note gives an example which shows they cannot be further extended to nonmetrizable Hausdorff locally solid linear topological Riesz spaces.References
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C. D. Aliprantis, On order and topological properties of Riesz spaces, Thesis, California Institute of Technology, 1973.
J. Hornáth, Topological vector spaces and distributions. I, Addison-Wesley, London, 1966.
- W. A. J. Luxemburg, Notes on Banach function spaces. XIVa, Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math. 27 (1965), 229–239. MR 0188766
- W. A. J. Luxemburg and A. C. Zaanen, Notes on Banach function spaces. IX, Nederl. Akad. Wetensch. Proc. Ser. A 67=Indag. Math. 26 (1964), 360–376. MR 0173167 —, Riesz spaces. I, North-Holland, Amsterdam, 1971.
- Hidegorô Nakano, Semi-ordered linear spaces, Japan Society for the Promotion of Science, Tokyo, 1955. MR 0073124
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 443-447
- MSC: Primary 46A40
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320692-9
- MathSciNet review: 0320692