Stability of Lipschitz-type functions under pointwise product and reciprocation
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-vanis...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/7724 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/7724 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.122 Lipschitz function Locally Lipschitz function Lipschitz in the small function Cauchy-Lipschitz function Pointwise product Reciprocation UC-space Cofinal completeness Modulus of continuity Análisis funcional y teoría de operadores Funciones (Matemáticas) Topología 1202 Análisis y Análisis Funcional 1210 Topología |
| Sumario: | 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. |
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