Topological properties of the efficient point set

Peleg, Bezalel

doi:10.1090/S0002-9939-1972-0303916-2

Topological properties of the efficient point set
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Proc. Amer. Math. Soc. 35 (1972), 531-536 Request permission

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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Efficiency prices in infinite dimensional spaces

A synthesis

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