Structure of the Efficient Point Set
نویسنده
چکیده
Let C be a nontrivial cone and Y be a set in the «-dimensional Euclidean space. Denote by E( Y|C) the set of all efficient points of X with respect to C. It will be proven that under some adequate assumptions E(Y|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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