Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some order and topological properties of locally solid linear topological Riesz spaces


Author: C. D. Aliprantis
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] C. D. Aliprantis, On order and topological properties of Riesz spaces, Thesis, California Institute of Technology, 1973.
  • [2] J. Hornáth, Topological vector spaces and distributions. I, Addison-Wesley, London, 1966.
  • [3] 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, Notes on Banach function spaces. XIVb, Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math. 27 (1965), 240–248. MR 0188767
    W. A. J. Luxemburg, Notes on Banach function spaces. XVa, Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math. 27 (1965), 415–429. MR 0188768
    W. A. J. Luxemburg, Notes on Banach function spaces. XVb, Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math. 27 (1965), 430–446. MR 0188769
    W. A. J. Luxemburg, Notes on Banach function spaces. XVIa, XVIb, Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math. 27 (1965), 646–657; 658–667. MR 0188770
  • [4] 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
    W. A. J. Luxemburg and A. C. Zaanen, Notes on Banach function spaces. X, XI, XII, XIII, Nederl. Akad. Wetensch. Proc. Ser. A 67=Indag. Math. 26 (1964), 493–506, 507–518, 519–529, 530–543. MR 0173168
  • [5] -, Riesz spaces. I, North-Holland, Amsterdam, 1971.
  • [6] Hidegorô Nakano, Semi-ordered linear spaces, Japan Society for the Promotion of Science, Tokyo, 1955. MR 0073124

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A40

Retrieve articles in all journals with MSC: 46A40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0320692-9
Keywords: Locally solid Riesz spaces, order and topological continuity
Article copyright: © Copyright 1973 American Mathematical Society