Generalized halfspaces in restricted-orientation convexity
نویسندگان
چکیده
منابع مشابه
Generalized halfspaces in restricted-orientation convexity
We first present some basic properties of O-halfspaces and compare them with the properties of standard halfspaces. We show that O-halfspaces may be disconnected, characterize an Ohalfspace in terms of its connected components, and derive the upper bound on the number of components. We then study properties of the boundaries of O-halfspaces. Finally, we describe the complements of O-halfspaces ...
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Restricted-orientation convexity (O-convexity) is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected. The notion of O-convexity generalizes standard convexity, as well as several other types of nontraditional convexity. We introduce and study O-halfspaces, which are analogs of standard halfspaces in the theory of O-convexity,...
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Restricted-orientation convexity (O-convexity) is the study of geometric objects whose intersections with lines from some xed set O of orientations are empty or connected. The notion of O-convexity generalizes standard convexity, as well as several other types of non-traditional convexity. We introduce and study O-halfspaces, which are analogs of standard halfspaces in the theory of O-convexity...
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Restricted-orientation convexity, also called O-convexity, is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We introduce restricted-orientation halfspaces, which are an O-convexity analog of halfspaces, explore their properties, and demonstrate their relationship to restricted-orientation convex sets.
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A restricted-orientation convex set, also called an O-convex set, is a set of points whose intersection with lines from some xed set is empty or connected. The notion of O-convexity generalizes standard convexity and orthogonal convexity. We explore some of the basic properties of O-convex sets in two and higher dimensions. We also study O-connected sets, which are restricted O-convex sets with...
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ژورنال
عنوان ژورنال: Journal of Geometry
سال: 1998
ISSN: 0047-2468,1420-8997
DOI: 10.1007/bf01237603