Generalized halfspaces in dimension groups
نویسندگان
چکیده
منابع مشابه
Generalized Halfspaces in Restricted-Orientation Convexityz
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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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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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2008
ISSN: 0168-0072
DOI: 10.1016/j.apal.2007.10.009