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...
| Autores: | , , , |
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| 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 |
| 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. |
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