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SMOOTH LIPSCHITZ RETRACTIONS OF STARLIKE BODIES ONTO THEIR BOUNDARIES IN INFINITE-DIMENSIONAL BANACH SPACES
Published online by Cambridge University Press: 25 July 2001
Abstract
Let X be an infinite-dimensional Banach space, and let A be a Cp Lipschitz bounded starlike body (for instance the unit ball of a smooth norm). We prove that:
(1) the boundary ∂A is Cp Lipschitz contractible;
(2) there is a Cp Lipschitz retraction from A onto ∂A;
(3) there is a Cp Lipschitz map T : A → A with no approximate fixed points.
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- © The London Mathematical Society 2001
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