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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Structure of the efficient point set
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by Đinh The Lục PDF
Proc. Amer. Math. Soc. 95 (1985), 433-440 Request permission

Abstract:

Let $C$ be a nontrivial cone and $X$ be a set in the $n$-dimensional Euclidean space. Denote by ${\text {E}}(X|C)$ the set of all efficient points of $X$ with respect to $C$. It will be proven that under some adequate assumptions ${\text {E}}(X|C)$ 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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • 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