RT Journal Article
T1 Stability of Lipschitz-type functions under pointwise product and reciprocation
A1 Beer, Gerald
A1 García-Lirola, Luis C.
A1 Garrido, M. Isabel
AB 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.
PB Springer
SN 1578-7303
YR 2020
FD 2020-04-25
LK https://hdl.handle.net/20.500.14352/7724
UL https://hdl.handle.net/20.500.14352/7724
LA eng
NO "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”.
NO Ministerio de Economía y Competitividad (MINECO)/FEDER
NO Ministerio de Ciencia, Innovación y Universidades (MCIU)
NO Región de Murcia; Fundación Séneca
DS Docta Complutense
RD 21 abr 2025