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Restricted-Orientation Convexity : Monographs in Theoretical Computer Science. An EATCS Series - Eugene Fink

Restricted-Orientation Convexity

Monographs in Theoretical Computer Science. An EATCS Series

Hardcover Published: 9th December 2003
ISBN: 9783540668152
Number Of Pages: 102

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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.

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From the reviews:

"The well-organized, readable, interesting volume considers two generalizations of the concept of convexity in Rn, 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)

Introductionp. 1
Two Dimensionsp. 9
Computational Problemsp. 21
Higher Dimensionsp. 35
Generalized Halfspacesp. 53
Strong Convexityp. 67
Closing Remarksp. 85
Referencesp. 93
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540668152
ISBN-10: 3540668152
Series: Monographs in Theoretical Computer Science. An EATCS Series
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 102
Published: 9th December 2003
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 0.79
Weight (kg): 0.76