Artículo
Cunto, A.F.; Losada, M.P.; Toranzos, F.A. "The visibility function revisited" (1999) Journal of Geometry. 65(1-2):101-110
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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. The basic intention of this paper is to extend this characterization to a compact subset of Ed. Under certain assumptions, it is proved here that the visibility function of such a set is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure. © Birkhäuser Verlag, 1999.
Registro:
| Documento: | Artículo |
| Título: | The visibility function revisited |
| Autor: | Cunto, A.F.; Losada, M.P.; Toranzos, F.A. |
| Filiación: | Departamento de Matemática, Universidad de Buenos Aires, Pabellón i - Ciudad Universitaria, 1428 Buenos Aires, Argentina |
| Año: | 1999 |
| Volumen: | 65 |
| Número: | 1-2 |
| Página de inicio: | 101 |
| Página de fin: | 110 |
| DOI: | http://dx.doi.org/10.1007/BF01228681 |
| Título revista: | Journal of Geometry |
| Título revista abreviado: | J. Geom. |
| ISSN: | 00472468 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00472468_v65_n1-2_p101_Cunto |
Referencias:
- Beer, G., The index of convexity and the visibility function (1973) Pacific J., 44, pp. 59-67
- Beer, G., The continuity of the visibility function of a starshaped set (1972) Canadian J., 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) Pub. Mat., 35, pp. 323-332
- 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
Citas:
---------- APA ----------
Cunto, A.F., Losada, M.P. & Toranzos, F.A. (1999) . The visibility function revisited. Journal of Geometry, 65(1-2), 101-110.http://dx.doi.org/10.1007/BF01228681
---------- CHICAGO ----------
Cunto, A.F., Losada, M.P., Toranzos, F.A. "The visibility function revisited" . Journal of Geometry 65, no. 1-2 (1999) : 101-110.http://dx.doi.org/10.1007/BF01228681
---------- MLA ----------
Cunto, A.F., Losada, M.P., Toranzos, F.A. "The visibility function revisited" . Journal of Geometry, vol. 65, no. 1-2, 1999, pp. 101-110.http://dx.doi.org/10.1007/BF01228681
---------- VANCOUVER ----------
Cunto, A.F., Losada, M.P., Toranzos, F.A. The visibility function revisited. J. Geom. 1999;65(1-2):101-110.http://dx.doi.org/10.1007/BF01228681
