Two theorems of Krasnosel′skiĭ type
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- by F. A. Valentine PDF
- Proc. Amer. Math. Soc. 18 (1967), 310-314 Request permission
References
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E. Helly, Über Mengen konvexer Körper mit gemeinshaftlichen Punkten, Jber. Deutsch. Math.-Verein. 32 (1923), 175-176.
- 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
- József Molnár, Über den zweidimensionalen topologischen Satz von Helly, Mat. Lapok 8 (1957), 108–114 (Hungarian, with German and Russian summaries). MR 100256 E. E. Robkin, Characterizations of starshaped sets, Doctoral Dissertation, Univ. of California, Los Angeles, 1965.
- E. E. Robkin and F. A. Valentine, Families of parallels associated with sets, Pacific J. Math. 16 (1966), 147–157. MR 187146, DOI 10.2140/pjm.1966.16.147
- Frederick A. Valentine, Convex sets, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Toronto-London, 1964. MR 0170264
Additional Information
- © Copyright 1967 American Mathematical Society
- 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