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On Levi-Like Properties and some of Their Applications in Riesz Space Theory

Published online by Cambridge University Press:  20 November 2018

G. Buskes  and
I. Labuda
G. Buskes
Affiliation:
Rljksuniversiteit Mathematisch Instituut Budapestlaan6, 3508 TA Utrecht, The Netherlands
I. Labuda
Affiliation:
Department of Mathematics, University of MississippiOxford, Mississippi 38677, U.S.A.
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Abstract

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Let (L, λ) be a locally solid Riesz space. (L, λ) is said to have the Levi property if for every increasing λ-bounded net (xα) ⊂ L+, sup xα exists. The Levi property, appearing in literature also as weak Fatou property (Luxemburg and Zaanen), condition (B) or monotone completeness (Russian terminology), is a classical object of investigation. In this paper we are interested in some variations of the property, their mutual relationships and applications in the theory of topological Riesz spaces. In the first part of the paper we clarify the status of two problems of Aliprantis and Burkinshaw. In the second part we study ideal-injective Riesz spaces.

Keywords

46A1006F20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 477 - 486
Copyright
Copyright © Canadian Mathematical Society 1988

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