Abstract:
In a recent paper, M. Breen has proved a Helly-type theorem for families of simple polygons in the plane. It is shown here that this result is a corollary of a well-known theorem of Molnár about families of compact and simply connected sets in the plane. A more general Helly-type theorem is established.
Registro:
Documento: |
Artículo
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Título: | Intersections of compact simply connected planar sets |
Autor: | Toranzos, F.A. |
Filiación: | Departamento de Matematica, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
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Palabras clave: | Helly-type theorems; Molnár's Theorem; Simple polygons |
Año: | 1997
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Volumen: | 66
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Número: | 5
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Página de inicio: | 349
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Página de fin: | 351
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Título revista: | Bulletin de la Societe Royale des Sciences de Liege
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Título revista abreviado: | Bull Soc R Sci Liege
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ISSN: | 00379565
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CODEN: | BSRSA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00379565_v66_n5_p349_Toranzos |
Referencias:
- Ambrosio, B., Consecuencias del teorems topológico de Helly (1990) Revista Un. Mat. Argentina, 35, pp. 13-18
- Breen, M., A Helly-type theorem for simple polygons (1996) Geom. Dedicata, 60, pp. 283-288
- Danzer, L., Grünbaum, B., Klee, V., Helly's theorem and its relatives (1963) Proc. Sympus. Pure Math., 7, pp. 101-180. , Amer. Math. Soc
- Helly, E., Über Systeme abgeschlossener Mengen mit gemeinshaftlichen (1930) Punkten, Monatsh. Math., 37, pp. 281-302
- Molnár, J., Über eine Verallgemeirung auf die Kügelflache eines topologische Satzes von Helly (1956) Acta Math. Acad. Sci. Hungar., 7, pp. 107-108
- Molnár, J., Über den zweidimensionalen topologische satz von Helly (1957) Math. Lapok, 8, pp. 311-314
- Robkin, E., (1965) Characterization of Starshaped Sets, , Doctoral Dissertation, U. C. L. A
Citas:
---------- APA ----------
(1997)
. Intersections of compact simply connected planar sets. Bulletin de la Societe Royale des Sciences de Liege, 66(5), 349-351.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00379565_v66_n5_p349_Toranzos [ ]
---------- CHICAGO ----------
Toranzos, F.A.
"Intersections of compact simply connected planar sets"
. Bulletin de la Societe Royale des Sciences de Liege 66, no. 5
(1997) : 349-351.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00379565_v66_n5_p349_Toranzos [ ]
---------- MLA ----------
Toranzos, F.A.
"Intersections of compact simply connected planar sets"
. Bulletin de la Societe Royale des Sciences de Liege, vol. 66, no. 5, 1997, pp. 349-351.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00379565_v66_n5_p349_Toranzos [ ]
---------- VANCOUVER ----------
Toranzos, F.A. Intersections of compact simply connected planar sets. Bull Soc R Sci Liege. 1997;66(5):349-351.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00379565_v66_n5_p349_Toranzos [ ]