ISSN:
1572-9168
Keywords:
generalized convexity
;
restricted orientations
;
higher dimensions.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Strong restricted-orientation convexity is a generalization of standard convexity. We explore the properties of strongly convex sets in multidimensional Euclidean space and identify major properties of standard convex sets that also hold for strong convexity. We characterize strongly convex flats and halfspaces, and establish the strong convexity of the affine hull of a strongly convex set. We then show that, for every point in the boundary of a strongly convex set, there is a supporting strongly convex hyperplane through it. Finally, we show that a closed set with nonempty interior is strongly convex if and only if it is the intersection of strongly convex halfspaces; we state a condition under which this result extends to sets with empty interior.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1004973709260
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