Publication: Cardinal coefficients related to surjectivity, darboux, and sierpiński-zygmund maps
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Publication Date
2017
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American Mathematical Society
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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.