From the reviews:
„The well-organized, readable, interesting volume considers two generalizations of the concept of convexity in R n , and their usual related concepts (hull, visibility, kernel, etc.). … The volume would be very good for a seminar studying the many results from the last two decades on these forms of generalized convexity. The book closes with suggestions and conjectures for the direction of future research.“ (John R. Reay, Mathematical Reviews, Issue 2007 j)
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.
