On a Question of Colin Clark Concerning Three Properties of Convex Sets(1)
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 535-537
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Let C be a convex subset of a normed linear space E. The following properties of C were studied by Clark [2]: (1) C is of finite width/ that is, C lies between two parallel closed hyperplanes; (2) C is of finite width in some direction; that is, for some line L in E there is a finite upper bound for the lengths of C's intersections with lines parallel to L; (3) C is partially bounded; that is, there is a finite upper bound for the radii of balls contained in C.
Klee, Victor. On a Question of Colin Clark Concerning Three Properties of Convex Sets(1). Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 535-537. doi: 10.4153/CMB-1972-094-9
@article{10_4153_CMB_1972_094_9,
author = {Klee, Victor},
title = {On a {Question} of {Colin} {Clark} {Concerning} {Three} {Properties} of {Convex} {Sets(1)}},
journal = {Canadian mathematical bulletin},
pages = {535--537},
year = {1972},
volume = {15},
number = {4},
doi = {10.4153/CMB-1972-094-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-094-9/}
}
TY - JOUR AU - Klee, Victor TI - On a Question of Colin Clark Concerning Three Properties of Convex Sets(1) JO - Canadian mathematical bulletin PY - 1972 SP - 535 EP - 537 VL - 15 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-094-9/ DO - 10.4153/CMB-1972-094-9 ID - 10_4153_CMB_1972_094_9 ER -
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