Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-02-11T21:25:36.197Z Has data issue: false hasContentIssue false
  • English
  • Français

A Proof of the Equivalence of Helly's and Krasnoselski's Theorems

Published online by Cambridge University Press:  20 November 2018

J. Borwein
J. Borwein*
Affiliation:
Dalhousie University, HalifaxN. S.
Rights & Permissions [Opens in a new window]

Abstract

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.

We show that Krasnoselski's Theorem, which is usually derived from Helly's Theorem, is in fact equivalent to it.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 35 - 37
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Eggleston, H. G., Convexity, Cambridge University Press, 1969.Google Scholar
2. Krasnoselski, M., Sur un crit?re pour qu'un domaine soit étoilée, Rec. Math. [Mat. Sbornik] N. S., 19 (1946), 309-310.Google Scholar
3. Toranzos, F. A., Radial functions of convex and star shaped sets, Amer. Math. Monthly, 74 (1967), 278-280.Google Scholar
4. Valentine, F. A., Convex Sets, McGraw-Hill, New York, 1964.Google Scholar