Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T04:37:39.631Z Has data issue: false hasContentIssue false
  • English
  • Français

A Banach Space Whose Elements are Classes of Sets of Constant Width

Published online by Cambridge University Press:  20 November 2018

J. E. Lewis
J. E. Lewis*
Affiliation:
Department of Mathematics, University of British Columbia Vancouver, B.C. Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let K be a compact subset of the real Euclidean space En. We say that K has constant width if the distance between each pair of distinct parallel hyperplanes which support K is constant. The collection of all compact convex subsets of En which have constant width is denoted .

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 679 - 689
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Berg, C., Shephard’s approximation theorem for convex bodies and the Milman Theorem Math. Scand. 25 (1969), 19–24.Google Scholar
2. Dunford, N. and Schwartz, J. T., Linear Operators, Part I. Interscience Publishers, Inc., New York (1957).Google Scholar
3. Eggleston, H. G., Convexity, Cambridge (1958).Google Scholar
4. Ewald, G. and Shephard, G. C., Normed vector spaces consisting of classes of convex sets. Math. Z. 91 (1966), 1–19.Google Scholar
5. Grunbaum, B., Convex Poly topes. Interscience Publishers, Inc., New York (1967).Google Scholar
6. Kelley, J. L., Namioka, I., et al., Linear Topological Spaces. D. Van Nostrand Co., Inc., Princeton (1963).Google Scholar
7. Shephard, G. C., Approximation problems for convex polyhedra. Mathematika, 11 (1964), 9–18.Google Scholar
8. Shephard, G. C., A pre-Hilbert space consisting of classes of convex subsets. Israel J. Math. 4 (1966), 1–10.Google Scholar
9. Wilanski, A., Functional analysis. Blaisdell Publ. Co., New York (1964).Google Scholar