Accession Number : AD0615041

Title :   CHARACTERIZATIONS OF STARSHAPED SETS.

Descriptive Note : Doctoral thesis,

Corporate Author : CALIFORNIA UNIV LOS ANGELES

Personal Author(s) : Robkin,Eugene Elliot

Report Date : JAN 1965

Pagination or Media Count : 83

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.

Descriptors :   (*SET THEORY, GEOMETRIC FORMS), CONICAL BODIES, SPHERES, CONVEX SETS, TOPOLOGY

Distribution Statement : APPROVED FOR PUBLIC RELEASE