Geodesic
On Levi-Like Properties and some of Their Applications in Riesz Space Theory
Canadian mathematical bulletin, Tome 31 (1988) no. 4, pp. 477-486

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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.
DOI : 10.4153/CMB-1988-069-3
Mots-clés : 46A10, 06F20 
Buskes, G.; Labuda, I. On Levi-Like Properties and some of Their Applications in Riesz Space Theory. Canadian mathematical bulletin, Tome 31 (1988) no. 4, pp. 477-486. doi: 10.4153/CMB-1988-069-3
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     title = {On {Levi-Like} {Properties} and some of {Their} {Applications} in {Riesz} {Space} {Theory}},
     journal = {Canadian mathematical bulletin},
     pages = {477--486},
     year = {1988},
     volume = {31},
     number = {4},
     doi = {10.4153/CMB-1988-069-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-069-3/}
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