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Subjects
52-XX Convex and discrete geometry
52Axx General convexity
52A15 Convex sets in $3$ dimensions (including convex surfaces)

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Sets invariant under projections onto two dimensional subspaces

Simon Fitzpatrick, Bruce Calvert (1991)

Commentationes Mathematicae Universitatis Carolinae

The Blaschke–Kakutani result characterizes inner product spaces $E$ , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace $F$ there is a norm 1 linear projection onto $F$ . In this paper, we determine which closed neighborhoods $B$ of zero in a real locally convex space $E$ of dimension at least 3 have the property that for every 2 dimensional subspace $F$ there is a continuous linear projection $P$ onto $F$ with $P (B) \subseteq B$ .

Singular sets of convex bodies and surfaces with generalized curvatures.

G. Anzellotti, E. Ossanna (1995)

Manuscripta mathematica

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