Restricted-Orientation Convexity

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Restricted-Orientation Convexity is written by Eugene Fink and published by Springer Science & Business Media. It's available with International Standard Book Number or ISBN identification 3642188494 (ISBN 10) and 9783642188497 (ISBN 13).

Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. We explore the properties of this generalized convexity in multidimensional Euclidean space, describes restricted-orientation analogs of lines, hyperplanes, flats, and halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. We then introduce the notion of strong restricted-orientation convexity, which is an alternative generalization of convexity, and show that its properties are also similar to those of standard convexity.