Pacific Journal of Mathematics

A quantitative version of Krasnosel'skiĭ 's theorem in ${\bf R}^{2}$.

Marilyn Breen

Article information

Pacific J. Math., Volume 91, Number 1 (1980), 31-37.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52A10: Convex sets in 2 dimensions (including convex curves) [See also 53A04]
Secondary: 52A35: Helly-type theorems and geometric transversal theory


Breen, Marilyn. A quantitative version of Krasnosel'skiĭ 's theorem in ${\bf R}^{2}$. Pacific J. Math. 91 (1980), no. 1, 31--37.

Export citation


  • [1] Marilyn Breen, The dimension of the kernel of a planar set, Pacific J. Math., (to appear).
  • [2] Marilyn Breen, K-dimensionalintersections of convex sets and convex kernels, Discrete Math., to appear.
  • [3] M. A. KrasnosePskii, Sur un critere pour qu'un domain soit etoile, Math. Sb., (61) 19 (1946), 309-310.
  • [4] S. Nadler, Hyper spaces of Sets, Marcel Dekker, Inc., New York, 1978.
  • [5] H. Tietze, Uber Konvexheitim kleinenund im grossen und iiber gewisse den Punkten einer Menge zugeordnete Dimensionzahlen,Math. Z., 29 (1928), 697-707.
  • [6] F. A. Valentine, Convex Sets, McGraw-Hill, New York, 1964.
  • [7] F. A. Valentine,Local convexity and Ln sets, Proc. Amer. Math. Soc, 16 (1965), 1305-1310.