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oai:docta.ucm.es:20.500.14352/77242025-12-10T11:22:32Zcom_20.500.14352_14col_20.500.14352_15

Stability of Lipschitz-type functions under pointwise product and reciprocation Beer, Gerald Garrido Carballo, María Isabel García-Lirola, Luis C. "This is a post-peer-review, pre-copyedit version of an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. The final authenticated version is available online at: http://dx.doi.org/10.1007/s13398-020-00847-x”. This article provides necessary and sufficient conditions on the structure of a metric space such that for various vector lattices of real-valued Lipschitz-type functions defined on the metric space, the vector lattice is stable under pointwise product, and such that the reciprocal of each non-vanishing member of the vector lattice remains in the vector lattice. In each case the family of metric spaces for which the first property holds contains the family of metric spaces for which the second property holds. At the end we prove some extension theorems for classes of locally Lipschitz functions that complement known results for Cauchy continuous functions and for uniformly continuous functions. 2023-06-17T08:57:42Z 2023-06-17T08:57:42Z 2020-04-25 journal article Beer, Gerald, et al. «Stability of Lipschitz-Type Functions under Pointwise Product and Reciprocation». Revista de La Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, vol. 114, n.o 3, julio de 2020, p. 120. DOI.org (Crossref), https://doi.org/10.1007/s13398-020-00847-x. 1578-7303 10.1007/s13398-020-00847-x https://hdl.handle.net/20.500.14352/7724 https://doi.org/10.1007/s13398-020-00847-x https://link.springer.com/article/10.1007/s13398-020-00847-x eng info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83262-C2-2-P/ES/LA INTERACCION ENTRE GEOMETRIA Y TOPOLOGIA EN ESPACIOS DE BANACH. APLICACIONES/ info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-097286-B-I00/ES/ANALISIS FUNCIONAL NO LINEAL Y GEOMETRICO/ open access Springer