caa a22 4500 38638570X CHVBK 20180307112057.0 cr unu---uuuuu 161130e198905 xx s 000 0 eng 10.1017/S0305004100077902 doi S0305004100077902 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100077902 Small Riesz spaces [Elektronische Daten] 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. Copyright © Cambridge Philosophical Society 1989 Buskes G. University of Mississippi, Mississippi MS 38677, U.S.A. van Rooij A. Katholieke Universiteit, 6525 ED Nijmegen, The Netherlands Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/3(1989-05), 523-536 0305-0041 105:3<523 1989 105 PSP https://doi.org/10.1017/S0305004100077902 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100077902 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Buskes G. University of Mississippi, Mississippi MS 38677, U.S.A NATIONALLICENCE 700 1- van Rooij A. Katholieke Universiteit, 6525 ED Nijmegen, The Netherlands NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/3(1989-05), 523-536 0305-0041 105:3<523 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 131163191 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge