Egoroff properties and the order topology in Riesz spaces-Reference-Cited by-同舟云学术

Egoroff properties and the order topology in Riesz spaces

Published:1974 Issue:0 Volume:187 Page:365-375
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Dodds Theresa K. Y. Chow

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1974-187-00/S0002-9947-1974-0336282-3/S0002-9947-1974-0336282-3.pdf

Reference18 articles.

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2. American Mathematical Society Colloquium Publications, Vol. XXV;Birkhoff, Garrett,1967

3. D. T. Egoroff, Sur les suites des fonctions measurables, C. R. Acad. Sci. Paris 152 (1911), 244-246.

4. Seminorms and the Egoroff property in Riesz spaces;Holbrook, John A. R.;Trans. Amer. Math. Soc.,1968

5. L. Kantorovitch, Lineare halbgeordnete Räume, Trans. Moscow Math. Soc. 44 (1937), 121-165.

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