|
A new representation of the Dedekind completion of  -spaces
Author(s):
Z.
Ercan;
S.
Onal
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3317-3321.
MSC (2000):
Primary 46A40;
Secondary 46B42, 54B42
Posted:
May 9, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
A new representation of the Dedekind completion of  is given. We present a necessary and sufficient condition on a compact Hausdorff space  for which the Dedekind completion of  is  , the space of real valued bounded functions on some set  .
References:
-
- 1.
- C. D. Aliprantis and O. Burkinshaw, Locally Solid Riesz spaces with Applications to Economics,
 Edition, Mathematical Surveys and Monographs, Volume 105, American Mathematical Society, Providence, RI, 2003. MR 2011364 - 2.
- R. P. Dilworth, The normal completion of the lattice of continuous functions, Trans. Amer. Math. Soc. 68 (1950), 427-438. MR 0034822 (11:647g)
- 3.
- W. Filter, Wolfgang Representations of Archimedean Riesz spaces-a survey, Rocky Mountain J. Math. 24 (1994), no. 3, 771-851.MR 1307578 (96f:46006)
- 4.
- S. Kaplan, The Bidual of
 I, North-Holland, New York and Amsterdam, 1985. MR 0776606 (86k:46001) - 5.
- S. Kaplan, Lebesgue Theory in the Bidual of
 , Memoirs Amer. Mat. Society 121 (1996), no. 579. MR 1329941 (96i:46023) - 6.
- W. A. J. Luxemburg and A.C. Zaanen, Riesz spaces I, North-Holland Publ. Comp., Amsterdam, 1971. MR 0511676 (58:23483)
- 7.
- J. E. Mack and D.G. Johnson, The Dedekind completion of
 , Pacific J. Math. 20 (1967), 231-243. MR 0211268 (35:2150) - 8.
- W. Maxey, The Dedekind completion of
 and its second dual, Ph.D. Thesis (1973), Purdue Univ. - 9.
- N. Nakano, Über das System aller stetigen Funktionen auf einen Topologischen Raum, Proc. Imp. Acad. (Tokyo) 17 (1941), 308-310.MR 0014173 (7:249f)
- 10.
- N. Nakano and T. Shimogaki, A note on the cut extension of C-spaces, Proc. Japan. Acad. 38 (1962), 473-477. MR 0149254 (26:6744)
- 11.
- A. I. Veksler, Functional representation of the order complement of a vector lattice of continuous functions, Sibirsk. Mat. Zh. 26 (1985), no. 6, 159-162. MR 0816514 (87j:46048a)
- 12.
- E. C. Weinberg, The alpha-completion of ring of continuous real-valued functions, Notices Amer. Math. Soc. 7 (1960), 533-534.
- 13.
- V. K. Zaharov, Functional characterization of absolute and Dedekind completion, Bull. Acad. Polon. Sci. Ser. Math. 29, no.5-6 (1981), 293-297. MR 0640475 (83b:54019)
- 14.
- V. K. Zaharov, Functional characterization of the absolute, vector lattices of functions with Baire property and of quasinormal functions and modules of particular continuous functions, Trudy Moskov. Mat. Obshch. 45 (1982), 68-104. MR 0704628 (85c:46033)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
46A40,
46B42, 54B42
Retrieve articles in all Journals with MSC
(2000):
46A40,
46B42, 54B42
Additional Information:
Z.
Ercan
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email:
zercan@metu.edu.tr
S.
Onal
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email:
osul@metu.edu.tr
DOI:
10.1090/S0002-9939-05-07889-5
PII:
S 0002-9939(05)07889-5
Keywords:
Riesz spaces,
Dedekind completion
Received by editor(s):
November 30, 2003
Received by editor(s) in revised form:
June 21, 2004
Posted:
May 9, 2005
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org