Cardinal coefficients related to surjectivity, Darboux, and Sierpinski-Zygmund maps


Krzysztof Chris Ciesielski J.L. Gamez-Merino, L. Mazza, and J.B. Seoane-Sepulveda,

Proc. Amer. Math. Soc. 145(3) (2017), 1041-1052.

We investigate the additivity A and lineability L cardinal coefficients 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 unusual big gap between the numbers A and L.

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Last modified December 20, 2016.