Additivity coefficients for all classes in the algebra of Darboux-Like maps on R

The class D of generalized continuous functions on R known under the common name of Darboux-like functions is usually described as consisting of eight families of maps: Darboux, connectivity, almost continuous, extendable, peripherally continuous, those having perfect road, and having either the Can...

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Detalles Bibliográficos
Autores: Ciesielski, K.C., Natkaniec, T., Rodríguez-Vidanes, D.L., Seoane Sepúlveda, Juan Benigno
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/7726
Acceso en línea:https://hdl.handle.net/20.500.14352/7726
Access Level:acceso abierto
Palabra clave:517
Additivity
lineability
Darboux-like functions
extendable functions.
Lineabilidad
Aditividad
Matemáticas (Matemáticas)
Análisis matemático
12 Matemáticas
1202 Análisis y Análisis Funcional
Descripción
Sumario:The class D of generalized continuous functions on R known under the common name of Darboux-like functions is usually described as consisting of eight families of maps: Darboux, connectivity, almost continuous, extendable, peripherally continuous, those having perfect road, and having either the Cantor Intermediate Value Property or the Strong Cantor Intermediate Value Property. The algebra A(D) of classes of functions generated by these families contains 17 atoms. In this work we will calculate the values of the additivity coefficient A(F) for all atoms F in the algebra A(D). We also determine the values A(F) for a lot of other families F∈A(D). Open questions and new directions of research shall also be provided.