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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Egoroff properties and the order topology in Riesz spaces


Author: Theresa K. Y. Chow Dodds
Journal: Trans. Amer. Math. Soc. 187 (1974), 365-375
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9947-1974-0336282-3
MathSciNet review: 0336282
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Abstract: In this paper we prove that, for a Riesz space L, the order closure of each subset of L coincides with its pseudo order closure if and only if the order closure of each convex subset of L coincides with its pseudo order closure; moreover, each of these statements is equivalent to the strong Egoroff property. For Archimedean Riesz spaces, similar results hold for the relative uniform topology.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0336282-3
Keywords: Riesz spaces, Egoroff property, order convergence, pseudo order closure, relative uniform convergence
Article copyright: © Copyright 1974 American Mathematical Society