Geodesic
Topological Completeness of Order Intervals in Riesz Spaces
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 316-323

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DOI

It is shown that if L is a Dedekind complete Riesz space equipped with a locally solid topology T defined by strongly (A, 0) Riesz pseudonorms, then order intervals of L are T-complete. This is an extension of a well known theorem of Nakano. The second part of the paper gives a necessary and sufficient condition for topological completeness of order intervals in a Dedekind σ-complete Riesz space which has a weak order unit and which is equipped with a locally solid σ-Fatou topology.
DOI : 10.4153/CMB-1984-048-1
Mots-clés : 46A40, 46A05 
Dodds, P. G. Topological Completeness of Order Intervals in Riesz Spaces. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 316-323. doi: 10.4153/CMB-1984-048-1
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     title = {Topological {Completeness} of {Order} {Intervals} in {Riesz} {Spaces}},
     journal = {Canadian mathematical bulletin},
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     year = {1984},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-048-1/}
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