Characterizations of Steiner points
Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 243-247
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To each convex compact $A$ in Euclidian space $E^n$ there corresponds a point $S(A)$ from $E^n$ such that 1) $S(x)=x$ for $x\in E^n$, 2) $S(A+B)=S(A)+S(B)$, 3) $S(A_i)\to0$, if $A_i$ converges in the Hausdorff metric to the unit sphere in $E^n$, then $S(A)$ is the Steiner point of the set $A$. The theorem improves certain earlier results on characterizations of the Steiner point.
@article{MZM_1973_14_2_a9,
author = {E. D. Positsel'skii},
title = {Characterizations of {Steiner} points},
journal = {Matemati\v{c}eskie zametki},
pages = {243--247},
publisher = {mathdoc},
volume = {14},
number = {2},
year = {1973},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a9/}
}
E. D. Positsel'skii. Characterizations of Steiner points. Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 243-247. http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a9/