Abstract
Presented to the Society, September 5, 1941 ; received by the editors May 6, 1941. 1 M. Eidelheit, Zur Theorie der konvexen Mengen in linear en normierten Râumen, Studia Mathematica, vol. 6 (1936), pp. 104-111. 2 Two sets are separated by a plane provided they lie in opposite closed halfspaces of the plane. 8 Added in proof: There has recently been brought to my attention another proof of Eidelheit's theorem by S. Kakutani, Proceedings of the Imperial Academy of Japan, vol. 13 (1937), pp. 93-94. The first part of the present proof is closely related to the first part of Kakutani's proof. 4 See S. Mazur, XJber konvexen Mengen in linearen normierten Râumen, Studia Mathematica, vol. 4 (1933), p. 74.
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