When lines go bad in hyperspace

• Autorzy: Bay C. , Lembcke A. , Schlicker S.
• Języki publikacji: EN

Abstrakty

EN

Let H(Rn) denote the hyperspace of all non-empty compact subsets of Rn. The Hausdorff metric h provides a way to measure distances between two elements of H(Rn) and generates the complete metric space (H(Rn),h)). In this paper, we examine geometric properties of lines in H(Rn), as determined by the Hausdorff metric, and compare and contrast the properties of these lines with Euclidean lines in Rn. Several surprising properties of these objects will be highlighted.

Słowa kluczowe

EN

hyperspace; Hausdorff metric; metric space

PL

hiperprzestrzeń; matryce Hausdorffa; przestrzeń metryczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 3
• Strony: 689--701
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Bay C.

• Truman State University

autor

Lembcke A.

• Concordia College

autor

Schlicker S.

• Department of Mathematics, Grand Valley State University, 2307 Mak, Allendale, Mi 49401-9403, USA

Bibliografia

• [1] Ch. Bay and S. Schlicker, The Geometry of 'H(Rn), Available at http.://faculty.gvsu.edu/schlicks/Chris-Report.pdf, August, 2003.
• [2] L. M. Blumenthal, Theory and Applications of Distance Geometry, Oxford University Press, 1953.
• [3] A. Bogdewicz, Some properties of hyperspaces, Demonstratio Math. 33 (2000), 135-149.
• [4] A. Bogdewicz, On affine and metric lines in the space of convex bodies, Rend. Circ. Mat. Palermo, 70 (2002), 57-78.
• [5] D. Braun, J. Mayberry, A. Powers, and S. Schlicker, The Geometry of the Hawdorff Metric, Available at http://faculty.gvsu.edu/schlicks/Hausdorf_paper.pdf, February, 2003.
• [6] L. Montejano, Convexity in the hyperspace of compact convex sets, An. Inst. Math. Univ. Nac. Autonoma Mexico, 26 (1986), 145-159.