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Cardinal coefficients related to surjectivity, darboux, and sierpiński-zygmund maps

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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

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


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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
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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