On universally complete Riesz spaces

Charalambos D. Aliprantis and Owen Sidney Burkinshaw

Vol. 71 (1977), No. 1, 1–12

DOI: 10.2140/pjm.1977.71.1

Abstract

In Math. Proc. Cambridge Philos. Soc. (1975), D. H. Fremlin studied the structure of the locally solid topologies on inextensible Riesz spaces. He subsequently conjectured that his results should hold true for σ-universally complete Riesz spaces.

In this paper we prove that indeed Fremlin’s results can be generalized to σ-universally complete Riesz spaces and at the same time establish a number of new properties. Examples of Archimedean universally complete Riesz spaces which are not Dedekind complete are also given.

Mathematical Subject Classification 2000

Primary: 46A40

Milestones

Received: 2 July 1976

Revised: 17 January 1977

Published: 1 July 1977