Infinitesimals in ordered vector spaces
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 1, pp. 18-22 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An infinitesimal approach to ordered spaces is proposed. Archimedean property and Dedekind completeness in ordered spaces are discussed from a nonstandard point of view.
@article{VMJ_2013_15_1_a2,
     author = {E. Yu. Emel'yanov},
     title = {Infinitesimals in ordered vector spaces},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {18--22},
     year = {2013},
     volume = {15},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a2/}
}
TY  - JOUR
AU  - E. Yu. Emel'yanov
TI  - Infinitesimals in ordered vector spaces
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 18
EP  - 22
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a2/
LA  - en
ID  - VMJ_2013_15_1_a2
ER  - 
%0 Journal Article
%A E. Yu. Emel'yanov
%T Infinitesimals in ordered vector spaces
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 18-22
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a2/
%G en
%F VMJ_2013_15_1_a2
E. Yu. Emel'yanov. Infinitesimals in ordered vector spaces. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 1, pp. 18-22. http://geodesic.mathdoc.fr/item/VMJ_2013_15_1_a2/

[1] Albeverio S., Høegh-Krohn R., Fenstad J. E., Lindstrøm T., Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Pure and Appl. Math., 122, Academic Press Inc., Orlando, 1986, xii+514 pp. | MR | Zbl

[2] Aliprantis C. D., Tourky R., Cones and Duality, Graduate Studies in Math., 84, Amer. Math. Soc., Providence (R.I.), 2007, xiv+279 pp. | MR | Zbl

[3] Emel'yanov E. Yu., “Ordered and regular hulls of vector lattices”, Siberian Math. J., 35:6 (1994), 1101–1108 | DOI | MR | Zbl

[4] Emel'yanov E. Yu., “Infinitesimals in vector lattices Nonstandard analysis and vector lattices”, Math. Appl., 525, Kluwer Acad. Publ., Dordrecht, 2000, 161–230 | MR

[5] Henson C. W., Moore L. C. (Jr.), “Nonstandard analysis and the theory of Banach spaces”, Nonstandard Analysis – Recent Developments, Lecture Notes in Math., 983, Springer, Berlin, 1983, 27–112 | DOI | MR

[6] Kusraev A. G., Kutateladze S. S., Nonstandard Methods of Analysis, Math. and Appl., 291, Kluwer Academic Publ., Dordrecht, 1994, viii+435 pp. | MR | Zbl

[7] Kutateladze S. S., Fundamentals of Functional Analysis, Kluwer Texts in the Math. Sciences, 12, Kluwer Academic Publ., Dordrecht, 1996, xiv+276 pp. | DOI | MR

[8] Luxemburg W. A. J., Zaanen A. C., Riesz Spaces, v. I, North-Holland, Amsterdam, 1971, xii+514 pp. | MR | Zbl

[9] Schaefer H. H., Wolff M. P., Topological Vector Spaces, Graduate Texts in Math., 3, 2nd edition, Springer-Verlag, New York, 1999, xii+346 pp. | DOI | MR

[10] Vulikh B. Z., Introduction to Theory of Cones in Normed Spaces, Kalinin State Univ., Kalinin, 1977, 84 pp.