Egoroff properties and the order topology in Riesz spaces
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- by Theresa K. Y. Chow Dodds PDF
- Trans. Amer. Math. Soc. 187 (1974), 365-375 Request permission
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.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- 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