Helly-Type Theorems for Roughly Convex-Like Sets
Phan Thanh An · Numerical Functional Analysis and Optimization · 2007
For a given positive real number γ, a subset M of an n-dimensional Euclidean space is said to be roughly convex-like (with the roughness degree γ) if x 0, x 1 ∊ M and ‖x 1 − x 0‖ > γ imply ]x 0, x 1[ ∩M ≠ . In this paper, we present Helly-type theorems for such sets and consider an open question about sets of constant width raised by Buchman and Valentine and Sallee (Croft, Falconer and Guy, Unsolved Problems in Geometry, Springer-Verlag, New York, 1991, pp. 131–132).