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).
• Version 1998-02-02_10 (18p) published version (19p)

@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}
}