Garrido, M. Isabel2023-06-192023-06-1920140004-972710.1017/S0004972714000215https://hdl.handle.net/20.500.14352/33803Let hX, di be a metric space. We characterise the family of subsets of X on which each locally Lipschitz function defined on X is bounded, as well as the family of subsets on which each member of two different subfamilies consisting of uniformly locally Lipschitz functions is bounded. It suffices in each case to consider real-valued functions.engjournal articlehttp://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9332599&fulltextType=RA&fileId=S0004972714000215http://journals.cambridge.org/action/displayJournal?jid=BAZrestricted access515.1Lipschitz functionLocally Lipschitz functionUniformly locally LipschitzFunctionLipschitz in the small functionfunction preserving Cauchy sequencesbornologytotally bounded setBourbaki bounded setTopología1210 Topología