# Article

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Keywords:
convex; projection; Hahn--Banach; subsets of \$\Bbb R^2\$
Summary:
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.
References:
[1] Schaeffer H.H.: Topological Vector Spaces. MacMillan, N.Y., 1966. MR 0193469

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