Artículo
Piacquadio Losada, M.; Forte Cunto, A.; Toranzos, F.A. "Continuity of the Visibility Function in the Boundary" (2000) Geometriae Dedicata. 80(1-3):43-49
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Abstract:
The visibility function of a compact set S ⊂ Ed assigns to each x ∈ S the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain. In a recent paper, the present authors extended this characterization to compact subsets of Ed with certain topological restrictions. These restrictions are removed here and it is proved that the visibility function of a compact subset of Ed is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure.
Registro:
| Documento: | Artículo |
| Título: | Continuity of the Visibility Function in the Boundary |
| Autor: | Piacquadio Losada, M.; Forte Cunto, A.; Toranzos, F.A. |
| Filiación: | Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| Palabras clave: | Beer's visibility function; Point of restricted visibility; Starshaped set |
| Año: | 2000 |
| Volumen: | 80 |
| Número: | 1-3 |
| Página de inicio: | 43 |
| Página de fin: | 49 |
| Título revista: | Geometriae Dedicata |
| Título revista abreviado: | Geom. Dedic. |
| ISSN: | 00465755 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00465755_v80_n1-3_p43_PiacquadioLosada |
Referencias:
- Beer, G., The index of convexity and the visibility function (1973) Pacific Math. J., 44, pp. 59-67
- Beer, G., The continuity of the visibility function on a starshaped set (1972) Canad. J. Math., 24, pp. 989-992
- Beer, G., Continuity properties of the visibility function (1973) Michigan Math. J., 20, pp. 297-302
- Forte Cunto, A., Continuity of the visibility function (1991) Publ. Mat., 35, pp. 323-332
- Forte Cunto, A., Piacquadio Losada, M., Toranzos, F.A., The visibility function revisited (1999) J. Geom., 65, pp. 101-110
- Stavrakas, N.M., The dimension of the convex kernel and points of local nonconvexity (1972) Proc. Amer. Math. Soc., 34, pp. 222-224
- Toranzos, F.A., Critical visibility and outward rays (1988) J. Geom., 33, pp. 155-167
- Valentine, F.A., (1964) Convex Sets, , McGraw-Hill, New York
- Von Neumann, J., (1950) Functional Operators, 1. , Princeton University Press, Princeton
Citas:
---------- APA ----------
Piacquadio Losada, M., Forte Cunto, A. & Toranzos, F.A. (2000) . Continuity of the Visibility Function in the Boundary. Geometriae Dedicata, 80(1-3), 43-49.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00465755_v80_n1-3_p43_PiacquadioLosada [ ]
---------- CHICAGO ----------
Piacquadio Losada, M., Forte Cunto, A., Toranzos, F.A. "Continuity of the Visibility Function in the Boundary" . Geometriae Dedicata 80, no. 1-3 (2000) : 43-49.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00465755_v80_n1-3_p43_PiacquadioLosada [ ]
---------- MLA ----------
Piacquadio Losada, M., Forte Cunto, A., Toranzos, F.A. "Continuity of the Visibility Function in the Boundary" . Geometriae Dedicata, vol. 80, no. 1-3, 2000, pp. 43-49.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00465755_v80_n1-3_p43_PiacquadioLosada [ ]
---------- VANCOUVER ----------
Piacquadio Losada, M., Forte Cunto, A., Toranzos, F.A. Continuity of the Visibility Function in the Boundary. Geom. Dedic. 2000;80(1-3):43-49.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00465755_v80_n1-3_p43_PiacquadioLosada [ ]
