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*, , is contractible. Furthermore, if 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0303916-2

Article copyright:
© Copyright 1972
American Mathematical Society