Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)

We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both topological and algebraical senses. Corresponding results are also obtained concern...

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Detalles Bibliográficos
Autores: Ayala Gómez, Rafael, Bernal González, Luis, Calderón Moreno, María del Carmen, Vilches Alarcón, José Antonio
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87513
Acceso en línea:https://hdl.handle.net/11441/87513
https://doi.org/10.1016/j.jmaa.2018.11.029
Access Level:acceso abierto
Palabra clave:Atsuji space
Non-uniformly continuous function
Lineability
Spaceability
Algebrability
Descripción
Sumario:We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both topological and algebraical senses. Corresponding results are also obtained concerning unbounded continuous functions on a non-compact metrizable space.