Separation theorems for sets in product spaces and equivalent assertions

Jörg Thierfelder

Kybernetika (1991)

  • Volume: 27, Issue: 6, page 522-534
  • ISSN: 0023-5954

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Thierfelder, Jörg. "Separation theorems for sets in product spaces and equivalent assertions." Kybernetika 27.6 (1991): 522-534. <http://eudml.org/doc/27449>.

@article{Thierfelder1991,
author = {Thierfelder, Jörg},
journal = {Kybernetika},
keywords = {separation and extension theorems in product spaces; vector optimization},
language = {eng},
number = {6},
pages = {522-534},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Separation theorems for sets in product spaces and equivalent assertions},
url = {http://eudml.org/doc/27449},
volume = {27},
year = {1991},
}

TY - JOUR
AU - Thierfelder, Jörg
TI - Separation theorems for sets in product spaces and equivalent assertions
JO - Kybernetika
PY - 1991
PB - Institute of Information Theory and Automation AS CR
VL - 27
IS - 6
SP - 522
EP - 534
LA - eng
KW - separation and extension theorems in product spaces; vector optimization
UR - http://eudml.org/doc/27449
ER -

References

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  2. J. M. Borwein, Continuity and differentiability properties of convex operators, Proc. London Math. Soc. 44 (1982), 3, 420-444. (1982) Zbl0487.46026MR0656244
  3. J. M. Borwein, On the Hahn-Banach extension property, Proc. Amer. Math. Soc. 86 (1982), 1,42-46. (1982) Zbl0499.46002MR0663863
  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. (1985) MR0822014
  5. R. B. Holmes, Geometric Functional Analysis and its Applications, Springer-Verlag, Berlin-Heidelberg-New York 1975. (1975) Zbl0336.46001MR0410335
  6. G. Jameson, Ordered Linear Spaces, (Lecture Notes in Mathematics, vol. 141.) Springer- Verlag, Berlin -Heidelberg-New York 1970. (1970) Zbl0196.13401MR0438077
  7. G. Köthe, Topologische Lineare Raume I, Springer-Verlag, Berlin-Heidelberg-New York 1966. (1966) MR0194863
  8. R. Nehse, The Hahn-Banach property and equivalent conditions, Comment. Math. Univ. Carolinae 19 (1978), 1, 165-177. (1978) Zbl0373.46011MR0492379
  9. R. Nehse, Separation of two sets in product spaces, Math. Nachrichten 97 (1980), 179-187. (1980) MR0600832
  10. R. Nehse, Zwei Fortsetzungssätze, Wiss. Zeitschrift TH Ilmenau 30 (1984), 49-57. (1984) Zbl0566.46002MR0749750
  11. A. L. Peressini, Ordered Topological Vector Spaces, Harper and Row, New York-Evanston-London 1967. (1967) Zbl0169.14801MR0227731
  12. J. Thierfelder, Nonvertical affine manifolds and separation theorems in product spaces (to appear) MR1121215
  13. 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. (1971) MR0417746
  14. M. Valadier, Sous-differentiabilité des fonctions convexes a valeurs dans un espace vectoriel ordoné, Math. Scand. 30 (1972), 65-74. (1972) MR0346525
  15. J. Zowe, Subdifferential of convex functions with values in ordered vector spaces, Math. Scand. 34(1974), 69-83. (1974) MR0380400

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