Ugrás a tartalomhoz

Convex Geometry

Csaba Vincze (2013)

University of Debrecen

5.2 Excercises

5.2 Excercises

Excercise 5.2.1 Prove that the kernel of D is convex.

Excercise 5.2.2 Find the kernels of the following shapes in the plane.

Excercise 5.2.3 Prove that the points

p 0 , z 0   a n d   u

in the proof of Krasnosselsky's theorem is not collinear.

Hint. In case of collinear points we have that p(0)=v(0) and z=z(0). Therefore H(0) separates the convex hull of B(p(0)) and u which is obviously a contradiction.

Figure 34: Kernels of sets in the plane.

Figure 35: The kernel as a singleton.