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A decomposition theorem for \(\aleph_1\)-convex sets. (English) Zbl 0498.52002

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A30 Variants of convex sets (star-shaped, (\(m, n\))-convex, etc.)
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References:

[1] Beer, G., Continuity properties of the visibility function, Michigan Math. J., 20, 297-302 (1973) · Zbl 0274.52010
[2] Breen, M.; Kay, D. C., General decomposition theorems for \(m\)-convex sets in the plane, Israel J. Math., 24, 217-233 (1976) · Zbl 0342.52006
[3] Eggleston, H. G., A condition for a compact plane set to be a union of finitely many convex sets, Proc. Cambridge Phil. Soc., 76, 61-66 (1974) · Zbl 0282.52003
[4] Kay, D. C.; Guay, M. D., Convexity and a certain property \(P_m\), Israel J. Math., 8, 39-52 (1970) · Zbl 0203.24701
[5] Valentine, F. A., A three point convexity property, Pacific J. Math., 7, 1227-1235 (1957) · Zbl 0080.15401
[6] Valentine, F. A., Convex Sets (1964), McGraw-Hill: McGraw-Hill New York · Zbl 0129.37203
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