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

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Ciesielski, K.C. and Natkaniec, T. and Rodríguez-Vidanes, D.L. and Seoane-Sepúlveda, Juan B. (2021) Additivity coefficients for all classes in the algebra of Darboux-Like maps on R. Results in mathematics, 76 (7). ISSN 1422-6383

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Official URL: https://doi.org/10.1007/s00025-020-01287-0



Abstract

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.


Item Type:Article
Uncontrolled Keywords:Additivity; lineability; Darboux-like functions; extendable functions.
Palabras clave (otros idiomas):Lineabilidad; Aditividad
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:63703
Deposited On:21 Jan 2021 11:55
Last Modified:21 Jan 2021 12:41

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