Literature cited
V. V. Makeev, “Universal coverings,” Ukr. Geom. Sb.,24, 70–79 (1981).
V. V. Makeev, “Application of topology to some problems of combinatorial geometry,” Ukr. Geom. Sb.,27, 50–57 (1984).
I. M. Yaglom and V. G. Boltyanskii, Convex Figures [in Russian], Gostekhizdat, Moscow (1951).
H. Yamabe and Z. Yujobo, “On the continuous functions defined on a sphere,” Osaka Math. J., No. 2, 19–22 (1950).
S. A. Kakutani, “A proof that there exists a circumscribing cube around any bounded closed convex set in R3,” Ann. Math.,43, 739–741 (1942).
F. J. Dyson, “Continuous functions defined on spheres,” Ann. Math.,54, 534–536 (1951).
G. R. Livesay, “Two theorems on the two-spheres (abstract),” Bull. Am. Math. Soc.,58, 492 (1952).
C. T. Yang, “On theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobo and Dyson. I,” Ann. Math.,60, 262–282 (1954).
C. T. Yang, “On theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujobo and Dyson. II,” Ann. Math.,62, 271–283 (1955).
D. C. Bourgin, “On some separation and mapping theorems,” Comment. Math. Helv.,29, 199–214 (1955).
B. Knaster, Colloquium Math.,1, 30–31 (1947).
L. Dancer, B. Grünbaum, and V. Klee, Helly's Theorem [Russian translation], Mir, Moscow (1968).
V. V. Makeev, “Dimensional restrictions in problems of combinatorial geometry,” Sib. Mat. Zh.,23, No. 4, 197–201 (1982).
V. G. Boltyanskii and I. P. Gokhberg, Theorems and Problems of Combinatorial Geometry [in Russian], Nauka, Moscow (1965).
B. Grünbaum, Studies on Combinatorial Geometry and the Theory of Convex Bodies [in Russian], Nauka, Moscow (1971).
S. S. Cairns, “Umbeschreibende Wurfel von convexen Körpern in euklidischen Räumen,” J. Reine Angew. Math.,208, No. 1, 91–101 (1961).
R. P. Jerrard, “Inscribed squares in plane conics,” Trans. Am. Math. Soc.,98, No. 2, 234–241 (1961).
N. Steenrod and D. Epstein, Cohomology Operations [Russian translation], Nauka, Moscow (1983).
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Translated from Matematicheskie Zametki, Vol. 36, No. 3, pp. 405–415, September, 1984.
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Makeev, V.V. Spatial generalizations of theorems on convex figures. Mathematical Notes of the Academy of Sciences of the USSR 36, 700–705 (1984). https://doi.org/10.1007/BF01141944
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DOI: https://doi.org/10.1007/BF01141944