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Abstract:

Several papers have appeared with descriptions of sets that are expressible as unions of 2 or 3 starshaped sets. The general problem is relevant since it is closely related to the classical "Art Gallery Problem". Some new solutions, for generic values of the parameters, are presented here. These solutions are adaptations of known characterizations of starshaped sets. © Birkhäuser Verlag, Basel, 2004.

Registro:

Documento: Artículo
Título:Sets expressible as finite unions of starshaped sets
Autor:Toranzos, F.A.; Cunto, A.F.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:Art gallery problem; Point of local nonconvexity; Union of starshaped sets
Año:2004
Volumen:79
Número:1-2
Página de inicio:190
Página de fin:195
DOI: http://dx.doi.org/10.1007/s00022-003-1563-8
Título revista:Journal of Geometry
Título revista abreviado:J. Geom.
ISSN:00472468
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00472468_v79_n1-2_p190_Toranzos

Referencias:

  • Breen, M., Clear visibility and unions of two starshaped sets in the plane (1984) Pacific J., 115, pp. 267-275
  • Breen, M., A Krasnosel'skii-type theorem for unions of two starshaped sets in the plane (1985) Pacific J., 120, pp. 19-31
  • Breen, M., Zamfirescu, T., A characterization theorem for certain unions of two starshaped sets in R2 (1987) Geom. Dedicata, 6, pp. 95-103
  • Breen, M., Characterizing compact unions of two starshaped sets in Rd (1989) J. Geom., 35, pp. 14-19
  • Breen, M., Unions of three starshaped sets in R2 (1989) J. Geom., 36, pp. 8-16
  • Koch, C.F., Marr, J.M., A characterization of unions of two star-shaped sets (1966) Proc. Amer. Math. Soc., 17, pp. 1341-1343
  • 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., Radial functions of convex and star-shaped bodies (1967) Amer. Math. Monthly, 74, pp. 278-280
  • Valentine, F.A., Local convexity and Ln sets (1965) Proc. Amer. Math. Soc., 16, pp. 197-202

Citas:

---------- APA ----------
Toranzos, F.A. & Cunto, A.F. (2004) . Sets expressible as finite unions of starshaped sets. Journal of Geometry, 79(1-2), 190-195.
http://dx.doi.org/10.1007/s00022-003-1563-8
---------- CHICAGO ----------
Toranzos, F.A., Cunto, A.F. "Sets expressible as finite unions of starshaped sets" . Journal of Geometry 79, no. 1-2 (2004) : 190-195.
http://dx.doi.org/10.1007/s00022-003-1563-8
---------- MLA ----------
Toranzos, F.A., Cunto, A.F. "Sets expressible as finite unions of starshaped sets" . Journal of Geometry, vol. 79, no. 1-2, 2004, pp. 190-195.
http://dx.doi.org/10.1007/s00022-003-1563-8
---------- VANCOUVER ----------
Toranzos, F.A., Cunto, A.F. Sets expressible as finite unions of starshaped sets. J. Geom. 2004;79(1-2):190-195.
http://dx.doi.org/10.1007/s00022-003-1563-8