Artículo
Abstract:
The notion of point of local nonconvexity has been an important tool in the study of the geometry of nonconvex sets, since Tietze characterized, more than fifty years ago, the convex subsets of En as those connected sets without points of local nonconvexity. It is proved here that for each convex component K of a closed connected set S in a locally convex space there exist points of local nonconvexity of S arbitrarily close to K, unless S itself be convex. Klee’s generalization of the just quoted Tietze’s theorem follows immediately. The notion of “higher visibility” is introduced in the last section, and three Erasnosselsky-type theorems involving the points of local nonconvexity are proved. © 1982, University of California, Berkeley. All Rights Reserved.
Registro:
| Documento: | Artículo |
| Título: | The points of local nonconvexity of starshaped sets |
| Autor: | Toranzos, F.A. |
| Filiación: | Facultad De Ciencias Exactas Y Naturales, Universidad De Buenos Aires, Koganei-Shi, Buenos Aires, Argentina |
| Año: | 1982 |
| Volumen: | 101 |
| Número: | 1 |
| Página de inicio: | 209 |
| Página de fin: | 213 |
| DOI: | http://dx.doi.org/10.2140/pjm.1982.101.209 |
| Título revista: | Pacific Journal of Mathematics |
| Título revista abreviado: | Pac. J. Math. |
| ISSN: | 00308730 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v101_n1_p209_Toranzos |
Referencias:
- Griinbaum, B., The dimension of intersections of convex sets (1962) Pacific J. Math., 12, pp. 197-202
- Helly, E., Uber Mengen konvexer Korper mit gemeinschaftlichen Punkten (1923) Jber. Deut- Sch. Math. Verein., 32, pp. 175-176
- Klee, V.L., Convex sets in linear spaces (1951) Duke Math. J., 18, pp. 443-466
- Klee, V.L., The critical set of a convex body (1953) Amer. J. Math., 75, pp. 178-188
- Tietze, H., Uber Konvexheit im kleinen und im grossen und uber gewisse den Punkten einer Menge zugeordnete Dimensionszahlen (1928) Math. Z., 28, pp. 697-707
- Toranzos, F.A., Radial functions of convex and starshaped bodies (1967) Amer. Math. Monthly, 74, pp. 278-280
- Valentine, F.A., Local convexity and Ln sets (1965) Proc. Of the Amer. Math. Soc., 16, pp. 1305-1310
Citas:
---------- APA ----------
(1982) . The points of local nonconvexity of starshaped sets. Pacific Journal of Mathematics, 101(1), 209-213.http://dx.doi.org/10.2140/pjm.1982.101.209
---------- CHICAGO ----------
Toranzos, F.A. "The points of local nonconvexity of starshaped sets" . Pacific Journal of Mathematics 101, no. 1 (1982) : 209-213.http://dx.doi.org/10.2140/pjm.1982.101.209
---------- MLA ----------
Toranzos, F.A. "The points of local nonconvexity of starshaped sets" . Pacific Journal of Mathematics, vol. 101, no. 1, 1982, pp. 209-213.http://dx.doi.org/10.2140/pjm.1982.101.209
---------- VANCOUVER ----------
Toranzos, F.A. The points of local nonconvexity of starshaped sets. Pac. J. Math. 1982;101(1):209-213.http://dx.doi.org/10.2140/pjm.1982.101.209
