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Proceedings of the American Mathematical Society

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On a theorem of Kōmura-Koshi and of Andô-Ellis

Author: Yau Chuen Wong
Journal: Proc. Amer. Math. Soc. 52 (1975), 227-231
MSC: Primary 46A40
MathSciNet review: 0377464
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Abstract: Kōmura and Koshi's result, which states that the topology $ \mathcal{I}$ of a nuclear locally convex vector lattice $ (E,C,\mathcal{I})$ is the topology $ o(E,E')$ of uniform convergence on all order-intervals in $ E'$, is generalized to the case when $ (E,C,\mathcal{I})$ is only a locally solid space. Andô-Ellis' theorem, concerning the duality of strict $ \mathfrak{B}$-cones and normality in normed vector spaces, is generalized to the metrizable case.

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Keywords: Solid, order-convex, decomposable, nuclear, base norm, strict $ \mathfrak{B}$-cones, normal cones, open decomposition, locally solid spaces, locally decomposable spaces, locally $ o$-convex spaces
Article copyright: © Copyright 1975 American Mathematical Society