On Unions of Two Convex Sets
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 883-886
Voir la notice de l'article provenant de la source Cambridge University Press
Valentine (3) introduced the three-point convexity property P 3 : a set S in En satisfies P 3 if for each triple of points x, y, z in S at least one of the closed segments xy, yz, xz is in S. He proved, (3 or 1) that in the plane a closed connected set satisfying P 3 is the union of some three convex subsets. The problem of characterizing those sets that are the union of two convex subsets was suggested. Stamey and Marr (2) have provided an answer for compact subsets of the plane. We present here a generalization of property P 3 which characterizes closed sets in an arbitrary topological linear space which are the union of two convex subsets.
McKinney, Richard L. On Unions of Two Convex Sets. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 883-886. doi: 10.4153/CJM-1966-088-7
@article{10_4153_CJM_1966_088_7,
author = {McKinney, Richard L.},
title = {On {Unions} of {Two} {Convex} {Sets}},
journal = {Canadian journal of mathematics},
pages = {883--886},
year = {1966},
volume = {18},
number = {1},
doi = {10.4153/CJM-1966-088-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-088-7/}
}
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[4] 4. Valentine, F. A., Convex sets (New York, 1964). Google Scholar
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