Pacific Journal of Mathematics

A Krasnosel'skiĭ-type theorem for unions of two starshaped sets in the plane.

Marilyn Breen

Article information

Source
Pacific J. Math., Volume 120, Number 1 (1985), 19-31.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102703880

Mathematical Reviews number (MathSciNet)
MR808926

Zentralblatt MATH identifier
0571.52006

Subjects
Primary: 52A30: Variants of convex sets (star-shaped, (m, n)-convex, etc.)

Citation

Breen, Marilyn. A Krasnosel'skiĭ-type theorem for unions of two starshaped sets in the plane. Pacific J. Math. 120 (1985), no. 1, 19--31. https://projecteuclid.org/euclid.pjm/1102703880


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References

  • [1] Marilyn Breen, An example concerning unions of two starshaped sets in the plane, Israel J. Math., 17 (1974), 347-349.
  • [2] Marilyn Breen, Clear visibility and unionsof two starshaped sets in theplane, Pacific J.Math., (to appear).
  • [3] Ludwig Danzer and Branko Grnbaum, Intersection properties of boxes in Rd, Combinatorica, 2 (3) (1982), 237-246.
  • [4] Ludwig Danzer, Branko Grunbaum and Victor Klee, Helly's theorem and its relatives, Proc. Symposia in Pure Math.,Vol. VII (Convexity) (1963), 101-180.
  • [5] Hugo Hadwiger, Hans Debrunner, and Victor Klee, Combinatorial Geometry in the Plane, Holt, Rinehart and Winston, New York,1964.
  • [6] M. A. Krasnosesk, Sur un criterepour qu'un domain soit etoile, Math. Sb., 19(61) (1946), 309-310.
  • [7] J. F. Lawrence, W. R. Hare, Jr., and John W. Kenelly, Finite unions of convex sets, Proc. Amer. Math. Soc,34 (1972), 225-228.
  • [8] Steven R. Lay, Convex Sets and TheirApplications, John Wiley, New York,1982.
  • [9] Godfried T. Toussaint and Hossan El-Gindy, Traditional galleries are star-shaped if every two paintings are visible from some common point, Amer. Math. Monthly, (to appear).
  • [10] F. A. Valentine, Convex Sets, McGraw Hill, New York, 1964.