Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T07:45:07.642Z Has data issue: false hasContentIssue false
  • English
  • Français

Description of most starshaped surfaces

Published online by Cambridge University Press:  28 June 2011

Tudor Zamfirescu
Tudor Zamfirescu
Affiliation:
Department of Mathematics, University of Dortmund, West Germany
Get access Rights & Permissions [Opens in a new window]

Extract

After having investigated in [7] generic properties of compact starshaped sets in ℝd, we shall restrict here our attention to compact starshaped sets whose kernels have positive dimension. While the main results in [7] are of a topological nature and concern the whole sets, the theorems presented here describe, for kernels of codimension 0 or 1, the local aspect of the boundaries and include, for kernels of positive dimension less than d— 1, both types of statements.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 245 - 251
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Breen, M.. Admissible kernels for starshaped sets. Proc. Amer. Math. Soc. 82 (1981), 622–628.CrossRefGoogle Scholar
[2] Gruber, P. and Zamfirescu, T.. Generic properties of compact starshaped sets. Proc. Amer. Math. Soc. (to appear).Google Scholar
[3] Klee, V.. Some new results on smoothness and rotundity in normed linear spaces. Math. Ann. 139 (1959), 51–63.CrossRefGoogle Scholar
[4] Klee, V.. A theorem on convex kernels. Mathematika 12 (1965), 89–93.CrossRefGoogle Scholar
[5] Post, K.. Star extension of plane convex sets. Indag. Math. 26 (1964), 330–338.CrossRefGoogle Scholar
[6] Zamfirescu, T.. Using Baire categories in geometry. Rend. Sem. Mat. Univ. Padova 43 (1985), 67–88.Google Scholar
[7] Zamfirescu, T.. Typical starshaped sets. Aequationes Math. 36 (1988), 188–200.CrossRefGoogle Scholar