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Functions with the Darboux property and functions with connected graphs. (English) Zbl 0095.26902

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[1] Bagemthl, F.: An example of a function with a distorted image. Mich. Math. J.4, 285-287 (1957). · Zbl 0081.04802 · doi:10.1307/mmj/1028997961
[2] Erdös, P., andS. Marcus: Sur la décomposition de l’espace euclidien en ensembles homogènes. Acta Math. Hung.8, 3-4, 443-452 (1957).
[3] Halperin, I.: Discontinuous functions with the Darboux property. Am. Math. Monthly57, 539-540 (1950). · Zbl 0040.17301 · doi:10.2307/2307938
[4] Halperin, I.: Non measurable sets and the equationf(x+y)=f(x)+f(y). Proc. Am. Math. Soc.2, 221-224 (1951). · Zbl 0043.11002
[5] Jones, F. B.: Connected and disconnected plane sets and the functional equationf(x+y)=f(x)+f(y). Bull. Am. Math. Soc.48, 115-120 (1942). · Zbl 0063.03063 · doi:10.1090/S0002-9904-1942-07615-4
[6] Kuratowski, C.: Topologie I. Warszawa-Wroclaw 1948.
[7] Kuratowski, C.: Topologie II. Warszawa 1952. · Zbl 0049.39704
[8] Kuratowski, C., etW. Sierpinski: Les fonctions de classe 1 et les ensembles connexes ponctiformes. Fundamenta Math.3, 304 (1922). · JFM 48.0277.04
[9] Kuratowski, C., etW. Sierpinski: Sur un problème de M. Fréchet concernant les dimensions des ensembles. Fundamenta Math.8, 193-200 (1926). · JFM 52.0587.01
[10] Kuratowski, C., etS. Ulam: Quelques propriétés topologiques du produit combinatoire. Fundamenta Math.19, 247-251 (1943).
[11] Maksimov, I.: Sur les fonctions ayant la propriété de Darboux. Prace Mat.-Fiz.43, 241-265 (1936). · Zbl 0013.25007
[12] Marcus, S.: Metric properties and descriptive properties for real functions of two variables (in Rumanian). Bul. ?tiintific Acad. R. P. R.5, 527-544 (1953).
[13] Marczewski, E.: Remarques sur les fonctions de Hamel. Colloq. Math.1, 249 (1948). · Zbl 0037.29110
[14] Sierpinski, W.: Leçons sur les nombres transfinis. Paris: Gauthier-Villars 1950, p. 131.
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