|
Whales and the universal completion
Author(s):
Gerard
Buskes;
Arnoud
van Rooij
Journal:
Proc. Amer. Math. Soc.
124
(1996),
423-427.
MSC (1991):
Primary 46A40
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we introduce whales in the collection of subsets of the Boolean algebra of bands in a Dedekind complete Riesz space and employ them to give a short (and constructive) proof of the existence of universal completions for Archimedean Riesz spaces.
References:
- 1
- Charalambos D. Aliprantis and Owen Burkinshaw, Locally solid Riesz spaces, Academic Press, New York, San Francisco, and London 1978. MR 58:12271
- 2
- ------, Positive operators, Academic Press, New York, 1985.MR 87h:47086
- 3
- Marlow Anderson and Todd Feil, Lattice ordered groups, an introduction, Reidel, Dordrecht, 1988.MR 90b:06001
- 4
- Simon J. Bernau, Lateral completion for arbitrary lattice groups, Bull. Amer. Math. Soc. 80 (1974), 334--336. MR 48:10938
- 5
- ------, The lateral completion of an arbitrary lattice group, J. Austral. Math. Soc. 19 (1975), 263--289.MR 52:5513
- 6
- ------, Lateral and Dedekind completion of Archimedean lattice groups, J. London Math. Soc. 12 (1975/76), 320--322. MR 53:5406
- 7
- G. Buskes and A. van Rooij, Riesz spaces and the ultrafilter theorem. I, Compositio Math. 83 (1992), 311--327. MR 93g:46006
- 8
- Paul Conrad, The lateral completion of a lattice-ordered group, Proc. London Math. Soc. 3 (1969), 444--480. MR 39:5442
- 9
- D. H. Fremlin, Inextensible Riesz spaces, Math. Proc. Cambridge Philos. Soc. 77 (1975), 71--89. MR 50:7995
- 10
- W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. I, North-Holland, Amsterdam, 1971. MR 58:23483
- 11
- B. de Pagter, The space of extended orthomorphisms in a Riesz space, Pacific J. Math. 112 (1984) 193--210.MR 85i:46013
- 12
- A. C. Zaanen, Another construction of the universal completion, Indag. Math. 45 (1983), 435--441. MR 85j:46011
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
46A40
Retrieve articles in all Journals with MSC
(1991):
46A40
Additional Information:
Gerard
Buskes
Affiliation:
Department of Mathematics, University of Mississippi, University, Mississippi 38677
Arnoud
van Rooij
Affiliation:
Mathematical Institute, The University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands
DOI:
10.1090/S0002-9939-96-02839-0
PII:
S 0002-9939(96)02839-0
Received by editor(s):
January 10, 1994
Received by editor(s) in revised form:
April 4, 1994
Additional Notes:
Both authors acknowledge partial support from NATO grant 940605.
Dedicated:
Dedicated to the memory of Bill Causey
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1996,
American Mathematical Society
|
Comments: webmaster@ams.org