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Stability of Lipschitz-type functions under pointwise product and reciprocation

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Beer, Gerald and García-Lirola, Luis C. and Garrido, M. Isabel (2020) Stability of Lipschitz-type functions under pointwise product and reciprocation. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 114 (3). ISSN 1578-7303

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Official URL: https://doi.org/10.1007/s13398-020-00847-x




Abstract

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.


Item Type:Article
Additional Information:

"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”.

Uncontrolled Keywords:Lipschitz function; Locally Lipschitz function; Lipschitz in the small function; Cauchy-Lipschitz function; Pointwise product; Reciprocation; UC-space; Cofinal completeness; Modulus of continuity
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Functions
Sciences > Mathematics > Topology
ID Code:63688
Deposited On:22 Jan 2021 15:05
Last Modified:25 Apr 2021 22:00

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