# Sh:675

- Shelah, S. (1997).
*On Ciesielski’s problems*. J. Appl. Anal.,**3**(2), 191–209. arXiv: math/9801155 DOI: 10.1515/JAA.1997.191 MR: 1619548 -
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). - 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}, doi = {10.1515/JAA.1997.191}, mrclass = {03E15 (03E05 03E35 26A03)}, mrnumber = {1619548}, mrreviewer = {Jakub Jasi\'nski}, doi = {10.1515/JAA.1997.191}, note = {\href{https://arxiv.org/abs/math/9801155}{arXiv: math/9801155}}, arxiv_number = {math/9801155} }