Works by Krzysztof Ciesielski

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1. Sierpiński-Zygmund functions that are Darboux, almost continuous, or have a perfect road.Marek Balcerzak, Krzysztof Ciesielski & Tomasz Natkaniec - 1997 - Archive for Mathematical Logic 37 (1):29-35.
In this paper we show that if the real line \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\Bbb R}$\end{document} is not a union of less than continuum many of its meager subsets then there exists an almost continuous Sierpiński–Zygmund function having a perfect road at each point. We also prove that it is consistent with ZFC that every Darboux function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $f\colon{\Bbb R}\to{\Bbb R}$\end{document} is continuous on some set (...)

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2. (1 other version)A model with no magic set.Krzysztof Ciesielski & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (4):1467-1490.
We will prove that there exists a model of ZFC+"c = ω 2 " in which every $M \subseteq \mathbb{R}$ of cardinality less than continuum c is meager, and such that for every $X \subseteq \mathbb{R}$ of cardinality c there exists a continuous function f: R → R with f[X] = [0, 1]. In particular in this model there is no magic set, i.e., a set $M \subseteq \mathbb{R}$ such that the equation f[M] = g[M] implies f = g for (...)