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Generalizations of two theorems of Janiszewski. I, II. (English) Zbl 0060.40402

Bull. Am. Math. Soc. 51, 954-960 (1945); ibid. 52, 478-480 (1946).

Keywords:

topology
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References:

[1] S. Eilenberg, Transformations continues en circonférence et la topologie du plan, Fund. Math. vol. 26 (1936) pp. 61-112. · Zbl 0013.42002
[2] Z. Janiszewski, Sur les coupures du plan faites par les continus (in Polish), Prace matematyczno-fizyczne vol. 26 (1913) pp. 11-63.
[3] F. Burton Jones, Certain consequences of the Jordan curve theorem, Amer. J. Math. 63 (1941), 531 – 544. · doi:10.2307/2371366
[4] B. Knaster and C. Kuratowski, Sur les continus non-bornés, Fund. Math. vol. 5 (1924) pp. 23-58.
[5] B. Knaster and C. Kuratowski, Sur les ensembles connexes, Fund. Math. vol. 2 (1921) pp. 206-255.
[6] C. Kuratowski and S. Straszewicz, Généralisation d’un théorème de Janiszewski, Fund. Math. vol. 12 (1928) pp. 152-157.
[7] C. Kuratowski, Sur la séparation d’ensembles situés sur le plan, Fund. Math. vol. 12 (1928) pp. 214-239.
[8] R. L. Moore, Foundations of point set theory, Revised edition. American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. · Zbl 0192.28901
[9] Anna M. Mullikin, Certain theorems relating to plane connected point sets, Trans. Amer. Math. Soc. 24 (1922), no. 2, 144 – 162.
[10] S. Nikodym, Sur les coupures du plan faites par les ensembles connexes et les continus, Fund. Math. vol. 7 (1925) pp. 15-23.
[11] S. Straszewicz, Über die Zerschneidung der Ebene durch abgeschlossene Mengen, Fund. Math. vol. 7 (1925) pp. 159-187.
[12] S. Straszewicz, Über eine Verallgemeinerung des Jordan’schen Kurvensatzes, Fund. Math. vol. 4 (1923) pp. 128-135.
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