On the completion of Hausdorff locally solid Riesz spaces
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- by Charalambos D. Aliprantis PDF
- Trans. Amer. Math. Soc. 196 (1974), 105-125 Request permission
Abstract:
In this paper we consider Hausdorff locally solid Riesz spaces $(L,\tau )$ and we denote by $(\hat L,\hat \tau )$ the Hausdorff topological completion of $(L,\tau )$. It is proved that $(\hat L,\hat \tau )$ is a Hausdorff locally solid Riesz space containing L as a Riesz subspace. We study the properties of $(L,\tau )$ which are inherited by $(\hat L,\hat \tau )$.References
- C. D. Aliprantis, Some order and topological properties of locally solid linear topological Riesz spaces, Proc. Amer. Math. Soc. 40 (1973), 443–447. MR 320692, DOI 10.1090/S0002-9939-1973-0320692-9 M. Duhoux, Le complété d’un treillis localement solide, Rapport n$^{o}$ 10, avril 1971, Séminaires de Mathématique Pure, Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain.
- D. H. Fremlin, On the completion of locally solid vector lattices, Pacific J. Math. 43 (1972), 341–347. MR 318832, DOI 10.2140/pjm.1972.43.341
- John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028
- Itizo Kawai, Locally convex lattices, J. Math. Soc. Japan 9 (1957), 281–314. MR 95399, DOI 10.2969/jmsj/00930281
- W. A. J. Luxemburg, Extensions of prime ideals and the existence of projections in Riesz spaces, Nederl. Akad. Wetensch. Proc. Ser A 76=Indag. Math. 35 (1973), 263–279. MR 0326343, DOI 10.1016/1385-7258(73)90013-9
- 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, DOI 10.1016/S1385-7258(65)50028-7
- W. A. J. Luxemburg and A. C. Zaanen, Notes on Banach function spaces. I, Nederl. Akad. Wetensch. Proc. Ser. A 66 = Indag. Math. 25 (1963), 135–147. MR 0149231, DOI 10.1016/S1385-7258(63)50014-6 —, Riesz spaces. I, North-Holland, Amsterdam, 1971.
- Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731
- Hidegorô Nakano, Semi-ordered linear spaces, Japan Society for the Promotion of Science, Tokyo, 1955. MR 0073124
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
- H. H. Schaefer, On the completeness of topological vector lattices, Michigan Math. J. 7 (1960), 303–309. MR 124712, DOI 10.1307/mmj/1028998441
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 196 (1974), 105-125
- MSC: Primary 46A40
- DOI: https://doi.org/10.1090/S0002-9947-1974-0350372-0
- MathSciNet review: 0350372