Abstract
Let be a metrizable topological space and let be a metric space. Let be a family of bounded continuous functions from to . We show that the family is Lipschitzian with respect to some compatible metric on if and only if the family can be written as a countable union of pointwise equicontinuous subfamilies. From this, we easily characterize those families of continuous functions between metrizable spaces that are Lipschitzian with respect to appropriately chosen metrics on the domain and target space.
Citation
Zvi Artstein. Gerald Beer. "MAKING CONTINUOUS FUNCTIONS LIPSCHITZ." Rocky Mountain J. Math. 54 (5) 1231 - 1240, October 2024. https://doi.org/10.1216/rmj.2024.54.1231
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