Pacific Journal of Mathematics

The dimension of the kernel of a planar set.

Marilyn Breen

Article information

Pacific J. Math., Volume 82, Number 1 (1979), 15-21.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52A30: Variants of convex sets (star-shaped, (m, n)-convex, etc.)
Secondary: 52A35: Helly-type theorems and geometric transversal theory


Breen, Marilyn. The dimension of the kernel of a planar set. Pacific J. Math. 82 (1979), no. 1, 15--21.

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  • [1] Marilyn Breen, Sets in Rd having (d--2)-dimensional kernels, Pacific J. Math., (to appear).
  • [2] N. E. Foland and J. M. Marr, Sets with zero dimensionalkernels, Pacific J. Math., 19 (1966), 429-432.
  • [3] W. R. Hare, Jr. and J. W. Kenelly, Concerning sets with one point kernel, Nieuw Arch. Wisk., 14 (1966), 103-105.
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  • [5] M. A. Krasnoseskii, Sur un critere pour qu'un domaine soit etoile, Math. Sb., (61) 19 (1946), 309-310.
  • [6] F. A. Toranzos, The dimension of the kernel of a starshaped set, Notices Amer. Math. Soc, 14 (1967), 832.