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Discrete Semi-Ordered Linear Spaces

Published online by Cambridge University Press:  20 November 2018

Israel Halperin  and
Hidegoro Nakano
Israel Halperin
Affiliation:
Queen's University
Hidegoro Nakano
Affiliation:
Tokyo University
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Let R be a semi-ordered linear space, that is, a vector lattice in Birkhoff's terminology [2]. An element a ∈ R is said to be discrete, if for every element x ∈ R such that there exists a real number a for which x = aa. For every pair of discrete elements a, b ∈ R we have or there exists a real number a for which b = aa or a = ab.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 293 - 298
Copyright
Copyright © Canadian Mathematical Society 1951

References

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