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Two theorems of Krasnoselskiĭ type


Author: F. A. Valentine
Journal: Proc. Amer. Math. Soc. 18 (1967), 310-314
MSC: Primary 52.30
DOI: https://doi.org/10.1090/S0002-9939-1967-0209976-X
MathSciNet review: 0209976
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  • [1] E. Helly, Über Mengen konvexer Körper mit gemeinshaftlichen Punkten, Jber. Deutsch. Math.-Verein. 32 (1923), 175-176.
  • [2] M. Krasnosselsky, Sur un critère pour qu’un domaine soit étoilé, Rec. Math. [Mat. Sbornik] N. S. 19(61) (1946), 309–310 (Russian, with French summary). MR 0020248
  • [3] József Molnár, Über den zweidimensionalen topologischen Satz von Helly, Mat. Lapok 8 (1957), 108–114 (Hungarian, with Russian and German summaries). MR 0100256
  • [4] E. E. Robkin, Characterizations of starshaped sets, Doctoral Dissertation, Univ. of California, Los Angeles, 1965.
  • [5] E. E. Robkin and F. A. Valentine, Families of parallels associated with sets, Pacific J. Math. 16 (1966), 147–157. MR 0187146
  • [6] Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR 0170264

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DOI: https://doi.org/10.1090/S0002-9939-1967-0209976-X
Article copyright: © Copyright 1967 American Mathematical Society