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arXiv · 2112.10265

Urysohn and Tietze extensions of Lipschitz functions

Ali Rejali·M. Azizi
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Abstract

Let (X,d) be a metric space and $ \alpha > 0 $. In this paper, we study extensions of some complex-valued Lipschitz functions, from some special subset $ X_0 $ to X. These extensions are with no-increasing Lipschitz number or the smallest Lipschitz number. Moreover, we show that under some conditions, Tietze extension theorem can be generalized for Lipschitz functions and call it Tietze-Lipschitz extension. Furthermore, we generalize Urysohn-lemma for Lipschitz functions. In fact we present a necessary and sufficient condition for that Lipschitz functions separate subsets of X.

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Ali Rejali, M. Azizi. 2021-12-19. Urysohn and Tietze extensions of Lipschitz functions. https://arxiv.org/abs/2112.10265

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