Lipschitz Extension of Multiple Banach-valued Functions in the Sense of Almgren
نویسنده
چکیده
A multiple-valued function f : X → QQ(Y ) is essentially a rule assigning Q unordered and non necessarily distinct elements of Y to each element of X. We study the Lipschitz extension problem in this context by using two general Lipschitz extension theorems recently proved by U. Lang and T. Schlichenmaier. We prove that the pair ` X,QQ(Y ) ́ has the Lipschitz extension property if Y is a Banach space and X is a metric space with a nite Nagata dimension. We also show that QQ(Y ) is an absolute Lipschitz retract if Y is a nite algebraic dimensional Banach space.
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