On some criteria of convexity for compact sets
\textit{G. Aumann} [Ann. Math. (2) 37, 443--447 (1936; Zbl 0014.03406)] showed that a compact set in \(\mathbb{R}^d\) is convex if all its intersections with planes of a fixed dimension are empty or homology cells. For later results see p. 26 of [\textit{P. Mani-Levitska}, Characterizations of convex sets, Handbook of convex geometry. Volume A. Amsterdam: North-Holland. 19--41 (1993; Zbl 0847.52001)] and [\textit{L. Montejano} and \textit{F. V. Shchepin}, Bull. Lond. Math. Soc. 28, No. 5, 501--504 (1996; Zbl 0863.52004)]. The present paper gives related results and extends them to quaternionic \(d\)-space.
scientific article; zbMATH DE number 6015949
scientific article