# Sh:675

• Shelah, S. (1997). On Ciesielski’s problems. J. Appl. Anal., 3(2), 191–209.
• 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\longrightarrow R there are functions g_n,h_n:R\longrightarrow 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 (\forall U\in [R]^{\aleph_1})(\exists U^*\in [U]^{\aleph_1}) (f\restriction U^* is continuous).
• Version 1998-02-02_10 (18p) published version (19p)
Bib entry
@article{Sh:675,
author = {Shelah, Saharon},
title = {{On Ciesielski's problems}},
journal = {J. Appl. Anal.},
fjournal = {Journal of Applied Analysis},
volume = {3},
number = {2},
year = {1997},
pages = {191--209},
issn = {1425-6908},
mrnumber = {1619548},
mrclass = {03E15 (03E05 03E35 26A03)},
doi = {10.1515/JAA.1997.191},
note = {\href{https://arxiv.org/abs/math/9801155}{arXiv: math/9801155}},
arxiv_number = {math/9801155}
}