Open Access
2000/2001 More on Compacta with Convex Projections
Stoyu Barov, Jan J. Dijkstra
Real Anal. Exchange 26(1): 277-284 (2000/2001).


We obtain information about the structure of nonconvex compacta $C$ in $\R^n$ ($n\ge3$) having the property that every projection onto a hyperplane is convex. We find that if $\dim(C)\le n-2$, then $C$ contains $n+1$ copies of $S^{n-2}$ that are contained in distinct hyperplanes. If $\dim(C)\ge n-1$, then the existence of three and no more than three hyperplanes that intersect $C$ in an $(n-2)$-sphere can be guaranteed.


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Stoyu Barov. Jan J. Dijkstra. "More on Compacta with Convex Projections." Real Anal. Exchange 26 (1) 277 - 284, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1044.52005
MathSciNet: MR1825509

Primary: 46A55 , 57N15

Keywords: compact set , convex set , facet , hyperplane , projection , Shadow

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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