On Ciesielski's problems
Logic
2016-09-07 v1
Abstract
We discuss some problems posed by Ciesielski. For example we show that, consistently, d_c is a singular cardinal and e_c<d_c. Next we prove that the Martin Axiom for sigma --centered forcing notions implies that for every function f:R^2 ---> R there are functions g_n,h_n:R ---> R, n< omega, such that f(x,y)= sum_{n=0}^{infty} g_n(x)h_n(y). Finally, we deal with countably continuous functions and we show that in the Cohen model they are exactly the functions f with the property that (for all U in [R]^{aleph_1})(exists U^* in [U]^{aleph_1}) (f restriction U^* is continuous).
Cite
@article{arxiv.math/9801155,
title = {On Ciesielski's problems},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9801155},
year = {2016}
}