Problem A. 775. (April 2020)

A. 775. Let \(\displaystyle H \subseteq \mathbb{R}^3\) such that if we reflect any point in \(\displaystyle H\) across another point of \(\displaystyle H\), the resulting point is also in \(\displaystyle H\). Prove that either \(\displaystyle H\) is dense in \(\displaystyle \mathbb{R}^3\) or one can find equidistant parallel planes which cover \(\displaystyle H\).

Submitted by Árpád Kurusa, Szeged and Vilmos Totik, Szeged

(7 pont)

Deadline expired on May 11, 2020.

Statistics:

2 students sent a solution.
7 points:	Weisz Máté.
0 point:	1 student.

Problems in Mathematics of KöMaL, April 2020