Abstract
In this chapter we prove the existence of some Lipschitz functions (the analog of Urysohn’s lemma for Lipschitz functions) and of Lipschitz partitions of unity. We also study algebraic operations with Lipschitz functions, sequences of Lipschitz functions, Lipschitz properties for differentiable functions (including a characterization in terms of Dini derivatives), and the possibility of gluing together Lipschitz functions. Applications are given to a sandwich type theorem, to Lipschitz selections for set-valued mappings and to the separability of the space C(T).
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Cobzaş, Ş., Miculescu, R., Nicolae, A. (2019). Basic Facts Concerning Lipschitz Functions. In: Lipschitz Functions. Lecture Notes in Mathematics, vol 2241. Springer, Cham. https://doi.org/10.1007/978-3-030-16489-8_2
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DOI: https://doi.org/10.1007/978-3-030-16489-8_2
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