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Let X be a compact metric space, and Lip(X) is the space of all bounded real-valued Lipschitz functions on X. A linear map T:Lip(X)->Lip(Y) is called disjointness preserving if fg=0 in Lip(X) implies TfTg=0 in Lip(Y). We prove that a biseparating linear bijection T(i.e. T and T^-1 are separating) is a weighted composition operator Tf=hf○φ, f is Lipschitz space from X onto R, φ is a homeomorphism from Y onto X, and h(y) is a Lipschitz function in Y.

Introduction...1
Preliminary...4
Main results...7

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