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Small Riesz spaces

Published online by Cambridge University Press:  04 October 2011

G. Buskes  and
A. van Rooij
G. Buskes
Affiliation:
University of Mississippi, Mississippi MS 38677, U.S.A.
A. van Rooij
Affiliation:
Katholieke Universiteit, 6525 ED Nijmegen, The Netherlands
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Extract

Many facts in the theory of general Riesz spaces are easily verified by thinking in terms of spaces of functions. A proof via this insight is said to use representation theory. In recent years a growing number of authors has successfully been trying to bypass representation theorems, judging them to be extraneous. (See, for instance, [9,10].) In spite of the positive aspects of these efforts the following can be said. Firstly, avoiding representation theory does not always make the facts transparent. Reading the more cumbersome constructions and procedures inside the Riesz space itself one feels the need for a pictorial representation with functions, and one suspects the author himself of secret heretical thoughts. Secondly, the direct method leads to repeating constructions of the same nature over and over again.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 523 - 536
Copyright
Copyright © Cambridge Philosophical Society 1989

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