  In Guo and Peng's article [Spherically convex sets and spherically convex
functions, J. Convex Anal. 28 (2021), 103--122], one defines the notions of
spherical convex sets and functions on "general curved surfaces" in
$\mathbb{R}^{n}$ $(n\ge2)$, one studies several properties of these classes of
sets and functions, and one establishes analogues of Radon, Helly,
Carath\'eodory and Minkowski theorems for spherical convex sets, as well as
some properties of spherical convex functions which are analogous to those of
usual convex functions. In obtaining such results, the authors use an analytic
approach based on their definitions. Our aim in this note is to provide simpler
proofs for the results on spherical convex sets; our proofs are based on some
characterizations/representations of spherical convex sets by usual convex sets
in $\mathbb{R}^{n}$.
