Artículo
Rodriguez, A.; Toranzos, F.A. "Structure of closed finitely starshaped sets mabel" (2000) Proceedings of the American Mathematical Society. 128(5):1433-1441
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Abstract:
A set S is finitely starshaped if any finite subset of S is totally visible from some point of S. It is well known that in a finite-dimensional linear space, a closed finitely starshaped set which is not starshaped must be unbounded. It is proved here that such a set must admit at least one direction of recession. This fact clarifies the structure of such sets and allows the study of properties of their visibility elements, well known in the case of starshaped sets. A characterization of planar finitely starshaped sets by means of its convex components is obtained. Some plausible conjectures are disproved by means of counterexamples. ©2000 American Mathematical Society.
Registro:
| Documento: | Artículo |
| Título: | Structure of closed finitely starshaped sets mabel |
| Autor: | Rodriguez, A.; Toranzos, F.A. |
| Filiación: | Instituto De Desarrollo Hljmano, Universidad Nacional De General Sarmiento, Roca 850, (1663), San Miguel, Argentina Departamento De MatemáTica, Universidad De Buenos Aires, Ciudad Universitaria, (1428) Buenos Aires, Argentina |
| Palabras clave: | Cone of recession; Convex components; Finitely starshapod sets |
| Año: | 2000 |
| Volumen: | 128 |
| Número: | 5 |
| Página de inicio: | 1433 |
| Página de fin: | 1441 |
| Título revista: | Proceedings of the American Mathematical Society |
| Título revista abreviado: | Proc. Am. Math. Soc. |
| ISSN: | 00029939 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez |
Referencias:
- Ambrosio, N.B., Consecuencias del teorema "topológico" de Helly (1990) Rev. Un. Mat. Argentina, 35, pp. 13-18
- Breen, M., Clear visibility, starshaped sets and finitely starshaped sets (1982) J. Geom., 19, pp. 183-196. , MR 84g:52013
- Brecn, M., Finitely starlike sets whose F-stars have positive measure (1989) J. Geom., 35, pp. 19-25
- Hansen, G.L., Unbounded convex sets: The enlarged affine space (1998) Rev. Mat. Fis. Teór. U. N. Tucumán, 32, pp. 217-234
- Helly, E., (1923) Mengen Konvexer Körper Mit Gemeinschaftlichen Punkten, Jahresber. Deutsch. Math. Verein., 32, pp. 175-176
- Jongmans, F., Etudes des cônes asociés à un ensemble (1983) Séminaire Stencilé, Liège, p. 1984
- Peterson, B.B., Is there a Krasnosel'skii theorem for finitely starlike sets? (1982) Convexity and Related Combinatorial Geometry, pp. 81-84. , Marcel Dekker, New York
- Rodriguez, M.A., Properties of external visibility (1997) Rev. Un. Mat. Argentina, 40, pp. 15-23. , MR 999a:52004
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- Toranzos, F.A., The points of local nonconvexity of starshaped sets (1982) Pacific J. Math., 101, pp. 209-214. , MR 984c:52013
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Citas:
---------- APA ----------
Rodriguez, A. & Toranzos, F.A. (2000) . Structure of closed finitely starshaped sets mabel. Proceedings of the American Mathematical Society, 128(5), 1433-1441.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez [ ]
---------- CHICAGO ----------
Rodriguez, A., Toranzos, F.A. "Structure of closed finitely starshaped sets mabel" . Proceedings of the American Mathematical Society 128, no. 5 (2000) : 1433-1441.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez [ ]
---------- MLA ----------
Rodriguez, A., Toranzos, F.A. "Structure of closed finitely starshaped sets mabel" . Proceedings of the American Mathematical Society, vol. 128, no. 5, 2000, pp. 1433-1441.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez [ ]
---------- VANCOUVER ----------
Rodriguez, A., Toranzos, F.A. Structure of closed finitely starshaped sets mabel. Proc. Am. Math. Soc. 2000;128(5):1433-1441.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v128_n5_p1433_Rodriguez [ ]
