convex; projection; Hahn--Banach; subsets of $\Bbb R^2$
The Hahn--Banach theorem implies that if $m$ is a one dimensional subspace of a t.v.s. $E$, and $B$ is a circled convex body in $E$, there is a continuous linear projection $P$ onto $m$ with $P(B)\subseteq B$. We determine the sets $B$ which have the property of being invariant under projections onto lines through $0$ subject to a weak boundedness type requirement.
 Schaeffer H.H.: Topological Vector Spaces
. MacMillan, N.Y., 1966. MR 0193469