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Proceedings of the American Mathematical Society

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

 
 

 

Topological properties of the efficient point set


Author: Bezalel Peleg
Journal: Proc. Amer. Math. Soc. 35 (1972), 531-536
MSC: Primary 90A99; Secondary 54F05, 90D99
DOI: https://doi.org/10.1090/S0002-9939-1972-0303916-2
MathSciNet review: 0303916
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Abstract: Let y be a closed and convex subset of a Euclidean space. We prove that the set of efficient points of Y, $ M(Y)$, is contractible. Furthermore, if $ M(Y)$ is closed (compact) then it is a retract of a convex closed (compact) set. Our proof relies on the Arrow-Barankin-Blackwell Theorem. A new proof is supplied for that theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0303916-2
Article copyright: © Copyright 1972 American Mathematical Society

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