Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-12T22:56:48.520Z Has data issue: false hasContentIssue false
  • English
  • Français

Order arguments on the dimension of vector lattices

Published online by Cambridge University Press:  14 November 2011

John T. Annulis
John T. Annulis
Affiliation:
Math Department, University of Arkansas-Monticello, Monticello, AR 71655, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

The main result asserts that the base of an infinite dimensional Dedekind complete space with unit contains an infinite set of disjoint elements. From this result it can be shown that the dimension of Dedekind σ -complete spaces with unit is not countably infinite.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 1-2 , 1981 , pp. 51 - 53
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Banach, S.. Opérations Linéaires, 2nd edn (New York: Chelsea, 1932).Google Scholar
2Luxemburg, W. A. J. and Zaanen, A. C.. Riesz Spaces I (Amsterdam: North-Holland, 1971).Google Scholar
3Peressini, A. L.. Ordered Topohgical Vector Spaces (New York: Harper and Row, 1967).Google Scholar
4Vulikh, B. Z.. Introduction to the Theory of Partially Ordered Spaces (Wolters-Noordhoff, Groningen, 1967).Google Scholar