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Title: Generalizing halfspaces
Authors: Fink, Eugene
Wood, Derick
Issue Date: Jun-1996
Series/Report no.: Computer Science Technical Report ; HKUST-CS96-27
Abstract: Restricted-orientation convexity is the study of geometric objects whose intersection with lines from some fixed set is empty or connected. We have studied the properties of restricted-orientation convex sets and demonstrated that this notion is a generalization of standard convexity. We now describe a restricted-orientation generalization of halfspaces and explore properties of these generalized halfspaces. In particular, we establish analogs of the following properties of standard halfspaces: the intersection of a halfspace with every line is empty, a ray, or a line; every halfspace is convex; a closed set with nonempty interior and convex boundary is a halfspace; the closure of the complement of a halfspace is a halfspace.
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