On Ciesielski's problems

Saharon Shelah

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arXiv · math/9801155

On Ciesielski's problems

Saharon Shelah

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Abstract

We discuss some problems posed by Ciesielski. For example we show that, consistently, d_c is a singular cardinal and e_c 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).

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Saharon Shelah. 1998-01-15. On Ciesielski's problems. https://arxiv.org/abs/math/9801155

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