| Title:
|
Separation theorems for sets in product spaces and equivalent assertions (English) |
| Author:
|
Thierfelder, Jörg |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
27 |
| Issue:
|
6 |
| Year:
|
1991 |
| Pages:
|
522-534 |
| . |
| Category:
|
math |
| . |
| MSC:
|
46A22 |
| MSC:
|
46A40 |
| MSC:
|
46A99 |
| MSC:
|
46N10 |
| MSC:
|
49J27 |
| MSC:
|
90C29 |
| idZBL:
|
Zbl 0778.46005 |
| idMR:
|
MR1150940 |
| . |
| Date available:
|
2009-09-24T18:28:43Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124294 |
| . |
| Reference:
|
[1] W. Bonnice, R. Silverman: The Hahn-Banach extension and the least upper bound properties are equivalent.Proc. Amer. Math. Soc. 18 (1967), 843 - 850. Zbl 0165.46802, MR 0215050 |
| Reference:
|
[2] J. M. Borwein: Continuity and differentiability properties of convex operators.Proc. London Math. Soc. 44 (1982), 3, 420-444. Zbl 0487.46026, MR 0656244 |
| Reference:
|
[3] J. M. Borwein: On the Hahn-Banach extension property.Proc. Amer. Math. Soc. 86 (1982), 1,42-46. Zbl 0499.46002, MR 0663863 |
| Reference:
|
[4] K.-H. Elster, J. Thierfelder: A general concept on cone approximations in nondifferentiable optimization.In: Nondifferentiable Optimization: Motivations and Applications (V. F. Demjanov; D. Pallaschke, eds.).(Lecture Notes in Economics and Mathematical Systems vol. 255.) Springer-Verlag, Berlin-Heidelberg-New York-Tokyo 1985, pp. 170-189. MR 0822014 |
| Reference:
|
[5] R. B. Holmes: Geometric Functional Analysis and its Applications.Springer-Verlag, Berlin-Heidelberg-New York 1975. Zbl 0336.46001, MR 0410335 |
| Reference:
|
[7] G. Jameson: Ordered Linear Spaces.(Lecture Notes in Mathematics, vol. 141.) Springer- Verlag, Berlin -Heidelberg-New York 1970. Zbl 0196.13401, MR 0438077 |
| Reference:
|
[8] G. Köthe: Topologische Lineare Raume I.Springer-Verlag, Berlin-Heidelberg-New York 1966. MR 0194863 |
| Reference:
|
[9] R. Nehse: The Hahn-Banach property and equivalent conditions.Comment. Math. Univ. Carolinae 19 (1978), 1, 165-177. Zbl 0373.46011, MR 0492379 |
| Reference:
|
[10] R. Nehse: Separation of two sets in product spaces.Math. Nachrichten 97 (1980), 179-187. MR 0600832 |
| Reference:
|
[11] R. Nehse: Zwei Fortsetzungssätze.Wiss. Zeitschrift TH Ilmenau 30 (1984), 49-57. Zbl 0566.46002, MR 0749750 |
| Reference:
|
[12] A. L. Peressini: Ordered Topological Vector Spaces.Harper and Row, New York-Evanston-London 1967. Zbl 0169.14801, MR 0227731 |
| Reference:
|
[13] J. Thierfelder: Nonvertical affine manifolds and separation theorems in product spaces (to appear). MR 1121215 |
| Reference:
|
[14] T. O. To: The equivalence of the least upper bound property and the Hahn-Banach property in ordered linear spaces.Proc. Amer. Math. Soc. 30 (1971), 287-295. MR 0417746 |
| Reference:
|
[15] M. Valadier: Sous-differentiabilité des fonctions convexes a valeurs dans un espace vectoriel ordoné.Math. Scand. 30 (1972), 65-74. MR 0346525 |
| Reference:
|
[16] J. Zowe: Subdifferential of convex functions with values in ordered vector spaces.Math. Scand. 34(1974), 69-83. MR 0380400 |
| . |
