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Ciesielski, Krzysztof Chris and Gámez Merino, José Luis and Mazza, L. and Seoane-Sepúlveda, Juan B.
(2017)
*Cardinal coefficients related to surjectivity, darboux, and sierpiński-zygmund maps.*
Proceedings of the American Mathematical Society, 145
(3).
pp. 1041-1052.
ISSN 0002-9939

PDF
Restringido a Repository staff only 241kB |

Official URL: http://www.ams.org/journals/proc/2017-145-03/S0002-9939-2016-13294-2/home.html

URL | URL Type |
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http://www.ams.org | UNSPECIFIED |

## Abstract

We investigate the additivity A and lineability L cardinal coeffiients for the following classes of functions: ES\SES of everywhere surjective functions that are not strongly everywhere surjective, Darboux-like, Sierpinski-Zygmund, surjective, and their corresponding intersections. The classes SES and ES have been shown to be 2c-lineable. In contrast, although we prove here that ES\SES is c+-lineable, it is still unclear whether it can be proved in ZFC that ES\SES is 2c-lineable. Moreover, we prove that if c is a regular cardinal number, then A(ES\SES) ≤ c. This shows that, for the class ES\SES, there is an unusually large gap between the numbers A and L.

Item Type: | Article |
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Uncontrolled Keywords: | Additivity, lineability, cardinal invariant, Darboux |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory Sciences > Mathematics > Functions |

ID Code: | 41510 |

Deposited On: | 27 Feb 2017 11:52 |

Last Modified: | 27 Feb 2017 12:13 |

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