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Abstract:

The notion of clear visibility has appeared recently in the literature concerning the geometry of starshaped sets. A somewhat converse notion, that of critical visibility, is explored here. As a by-product it is proved that the points of local nonconvexity of a closed connected set S determine the nontrivial portions of the boundary of the star of a point in S. Paragraph 4 is devoted to the study of the concepts of outward ray through a boundary point and inner stem of that point. A new characterization of the convex kernel of a starshaped set results from this study, and Krasnoselsky-type theorems are obtained in the planar case. © 1988 Birkhäuser Verlag.

Registro:

Documento: Artículo
Título:Critical visibility and outward rays
Autor:Toranzos, F.A.
Filiación:Departamento de Matematica, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Año:1988
Volumen:33
Número:1-2
Página de inicio:155
Página de fin:167
DOI: http://dx.doi.org/10.1007/BF01230614
Título revista:Journal of Geometry
Título revista abreviado:J Geom
ISSN:00472468
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00472468_v33_n1-2_p155_Toranzos

Referencias:

  • Breen, M., The dimension of the kernel of a planar set (1979) Pacific Journal of Mathematics, 82, pp. 15-21
  • Breen, M., A Krasnosels'kii-type theorem for points of local nonconvexity (1982) Proc. of the Amer. Math, Sac., 85, pp. 261-265
  • Breen, M., Clear visibility and the dimension of kernels of starshaped sets (1982) Proceedings of the American Mathematical Society, 85, pp. 414-418
  • Falconer, K.J., The dimension of the convex kernel of a compact starshaped set (1977) Bulletin of the London Mathematical Society, 9, pp. 313-316
  • Grunbaum, B., The dimension of intersections of convex sets (1962) Pacific Journal of Mathematics, 12, pp. 197-202
  • Helly, E., Über Mengen konvexer Körper mit gemeinschaftlichen Punkten (1923) Jber. Deutsch Math. Verein., 32, pp. 175-176
  • Klee, V.L., The critical set of a convex body (1953) American Journal of Mathematics, 75, pp. 178-188
  • Krasnoselsky, M.A., Sur un critēre pour qu'un domaine soit ētoilē (1946) Math. Sb., 19, pp. 309-310
  • Stavrakas, N.M., The dimension of the convex kernel and points of local nonconvexity (1972) Proceedings of the American Mathematical Society, 34, pp. 222-224
  • Toranzos, F.A., Radial functions of convex and starshaped bodies (1967) The American Mathematical Monthly, 74, pp. 278-280
  • Toranzos, F.A., The points of local nonconvexity of star-shaped sets (1982) Pacific Journal of Mathematics, 101, pp. 209-214
  • VALENTINE, F. A.: Convex sets. New York, 1964; Valentine, F.A., Local convexity andL<inf>n</inf>sets (1965) Proc. of the Amer. Math. Soc., 16, pp. 1305-1310
  • Valentine, F.A., Local convexity and starshaped sets (1965) Israel J. of Math., 3, pp. 39-42

Citas:

---------- APA ----------
(1988) . Critical visibility and outward rays. Journal of Geometry, 33(1-2), 155-167.
http://dx.doi.org/10.1007/BF01230614
---------- CHICAGO ----------
Toranzos, F.A. "Critical visibility and outward rays" . Journal of Geometry 33, no. 1-2 (1988) : 155-167.
http://dx.doi.org/10.1007/BF01230614
---------- MLA ----------
Toranzos, F.A. "Critical visibility and outward rays" . Journal of Geometry, vol. 33, no. 1-2, 1988, pp. 155-167.
http://dx.doi.org/10.1007/BF01230614
---------- VANCOUVER ----------
Toranzos, F.A. Critical visibility and outward rays. J Geom. 1988;33(1-2):155-167.
http://dx.doi.org/10.1007/BF01230614