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Some Characterizations of Dedekind α-Completeness of a Riesz Space

Published online by Cambridge University Press:  20 November 2018

Y. A. Abramovich  and
A. W. Wickstead
Y. A. Abramovich
Affiliation:
Department of Mathematics IUPUI Indianapolis, Indiana 46205 USA
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Abstract

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A vector lattice F is said to be Dedekind α-complete, where α is a cardinal number, provided that each non-empty order bounded subset D of F satisfying card(D) ≤ α has a supremum. Several characterizations of this property are presented here.

Keywords

47B5546A40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 3 - 7
Copyright
Copyright © Canadian Mathematical Society 1993

References

[A] Abramovich, Y. A., On some properties of norm in normed lattices and their maximal normed extensions, Thesis, Leningrad State Univ., 1972.Google Scholar
[AB] Aliprantis, C. D. and Burkinshaw, O., Positive Operators, Pure and Applied Mathematics (119), Academic Press, New York & London, 1985.Google Scholar
[AG] Abramovich, Y. A. (Ju. A. Abramovič) and Gejler, V. A., On a question of Fremlin concerning order bounded and regular operators, Coll. Math. 46(1982), 15–17.Google Scholar
[AV] Abramovich, Y. A. and Veksler, A. I., Exploring partially ordered spaces by means of transfinite sequences, Optimizacija, Novosibirsk (129), (1973), 8–17.Google Scholar
[AW]Y Abramovich, A. and Wickstead, A. W., Regular operators from and into a small Riesz space, Indag. Math. 2(1991), 257–274.Google Scholar
[KVP] Kantorovich, L. V., Vulikh, B. Z. and Pinsker, A. G., Functional Analysis in partially ordered spaces, Moskow, 1950.Google Scholar
[LZ]W. Luxemburg, A. J. and Zaanen, A. C., Riesz spaces I, North Holland, Amsterdam, 1971.Google Scholar
[SSaito, W. K. and Maitland, J. D. Wright, All AW*-Factors are Normal, J. London Math. Soc. (2) 44(1991), 143–154.Google Scholar
[V] Vulikh, B. Z., Introduction to the theory of partially ordered spaces, Walters-Noordoff Sci. Publication, Groningen, 1967.Google Scholar
[VG] Veksler, A. I. and V Gejler, A., Order and disjoint completeness of linear partially ordered spaces, Sibirsk. Math. J. 13(1972), 43–51.Google Scholar
[W] Wickstead, A. W., The regularity of order bounded operators into C(K), Quart. J. Math. Oxford (2) 41(1990), 359–368.Google Scholar