Open AccessCardinal coefficients related to surjectivity, Darboux, and Sierpiński-Zygmund maps
Author(s) -
Krzysztof Ciesielski,
José L. Gámez-Merino,
Lucian Mazza,
Juan B. SeoaneSepúlveda
Publication year - 2016
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/13294
Subject(s) - algorithm , annotation , type (biology) , artificial intelligence , computer science , surjective function , mathematics , discrete mathematics , geology , paleontology
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