  We study the Weihrauch degrees of closed choice for finite sets, closed
choice for convex sets and sorting infinite sequences over finite alphabets.
Our main results are: One, that choice for finite sets of cardinality $i + 1$
is reducible to choice for convex sets in dimension $j$, which in turn is
reducible to sorting infinite sequences over an alphabet of size $k + 1$, iff
$i \leq j \leq k$. Two, that convex choice in dimension two is not reducible to
the product of convex choice in dimension one with itself. Three, that
sequential composition of one-dimensional convex choice is not reducible to
convex choice in any dimension. The latter solves an open question raised at a
Dagstuhl seminar on Weihrauch reducibility in 2015. Our proofs invoke Kleene's
recursion theorem, and we describe in some detail how Kleene's recursion
theorem gives rise to a technique for proving separations of Weihrauch degrees.
