Generalized halfspaces in restricted-orientation convexity
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چکیده
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 and give a necessary and sufficient condition under which the complement of an O-halfspace is an O-halfspace.
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تاریخ انتشار 1995