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Description of most starshaped surfaces

Published online by Cambridge University Press:  28 June 2011

Tudor Zamfirescu
Affiliation:
Department of Mathematics, University of Dortmund, West Germany

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
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

[1] Breen, M.. Admissible kernels for starshaped sets. Proc. Amer. Math. Soc. 82 (1981), 622628.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), 5163.CrossRefGoogle Scholar
[4] Klee, V.. A theorem on convex kernels. Mathematika 12 (1965), 8993.CrossRefGoogle Scholar
[5] Post, K.. Star extension of plane convex sets. Indag. Math. 26 (1964), 330338.CrossRefGoogle Scholar
[6] Zamfirescu, T.. Using Baire categories in geometry. Rend. Sem. Mat. Univ. Padova 43 (1985), 6788.Google Scholar
[7] Zamfirescu, T.. Typical starshaped sets. Aequationes Math. 36 (1988), 188200.CrossRefGoogle Scholar