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Abstract:
In 1946 Krasnosel'skii characterized compact starshaped sets in n-dimensional Euclidean space En M. A. Krasnosel'skii, 'Sur un critere pour qu'un domain soit etoils' (Russian, French summary), Mat. Sb. (N. S.), vol. 19 (61)(1946), pp. 309-310. In doing this he utilized the notions of 'regular point' and 'visibility' together with Helly's Theorem (E. Helly, 'Uber Mengen konvexer Korper mit gemeinschaftlicher Punkten,' Jber. Deutsch. Math. Verein, vol. 32 (1923), pp. 175-176). The author introduces several new concepts which together with Helly's Theorem and some of its relatives (L. Danzer, B. Brunbaum, and V. Klee, 'Helly's Theorem and its relatives,' American Mathematical Society Symposium on Convexity, Seattle, Proc. Symp. Pure Math., vol 7, 1963) enables him to characterize several classes of starshaped sets.
| Description: |
Doctoral thesis |
| Pages: |
83 |
| Report Date: |
JAN 1965 |
| Contract Number: |
Nonr23376 |
| Report Number: |
0140516 |
Report Unavailable |
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