Structure of the efficient point set

Author:
Đinh The Lục

Journal:
Proc. Amer. Math. Soc. **95** (1985), 433-440

MSC:
Primary 49A50; Secondary 90A14, 90C31

DOI:
https://doi.org/10.1090/S0002-9939-1985-0806083-0

MathSciNet review:
806083

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Abstract: Let be a nontrivial cone and be a set in the -dimensional Euclidean space. Denote by the set of all efficient points of with respect to . It will be proven that under some adequate assumptions is homeomorphic to a simplex while , and for it is a contractible set. Furthermore, the set of all weak efficient points of with respect to is arcwise connected and its local contractibility is equivalent to being a retract of . The results presented in this study cover all topological properties of the efficient point set which have been obtained by Peleg and Morozov for the case when is the nonnegative orthant.

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0806083-0

Article copyright:
© Copyright 1985
American Mathematical Society