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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 $ C$ be a nontrivial cone and $ X$ be a set in the $ n$-dimensional Euclidean space. Denote by $ {\text{E}}(X\vert C)$ the set of all efficient points of $ X$ with respect to $ C$. It will be proven that under some adequate assumptions $ {\text{E}}(X\vert C)$ is homeomorphic to a simplex while $ n = 2$, and for $ n > 2$ it is a contractible set. Furthermore, the set of all weak efficient points of $ X$ with respect to $ C$ is arcwise connected and its local contractibility is equivalent to being a retract of $ X$. 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 $ C$ 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

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