A. Kharazishvili

On Maximal $ot$-Subsets of the Euclidean Plane

We say that a subset $X$ of the plane ${\bf R}^2$ is an $ot$-set if any three points of $X$ form an obtuse triangle. Some properties of $ot$-sets are investigated. It is shown that no finite $ot$-subset of
${\bf R}^2$ is maximal, but there exists a countable maximal $ot$-subset of ${\bf R}^2$. Several related problems are formulated and discussed.