Geodesic
Separation of $(n+1)$-families of sets in general position in $\bold R^n$
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 743-748

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper the main result in [1], concerning $(n+1)$-families of sets in general position in ${\bold R}^n$, is generalized. Finally we prove the following theorem: If $\{A_1,A_2,\dots,A_{n+1}\}$ is a family of compact convexly connected sets in general position in ${\bold R}^n$, then for each proper subset $I$ of $\{1,2,\dots,n+1\}$ the set of hyperplanes separating $\cup\{A_i: i\in I\}$ and $\cup\{A_j: j\in \overline{I}\}$ is homeomorphic to $S_n^+$.
Classification : 47H10, 52A37
Keywords: family of sets in general position; convexly connected sets; Fan-Glicksberg-Kakutani fixed point theorem 
@article{CMUC_1997__38_4_a9,
     author = {Balaj, Mircea},
     title = {Separation of $(n+1)$-families of sets in general position in $\bold R^n$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {743--748},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {1997},
     mrnumber = {1603706},
     zbl = {0946.52002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a9/}
}
TY  - JOUR
AU  - Balaj, Mircea
TI  - Separation of $(n+1)$-families of sets in general position in $\bold R^n$
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1997
SP  - 743
EP  - 748
VL  - 38
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a9/
LA  - en
ID  - CMUC_1997__38_4_a9
ER  - 
%0 Journal Article
%A Balaj, Mircea
%T Separation of $(n+1)$-families of sets in general position in $\bold R^n$
%J Commentationes Mathematicae Universitatis Carolinae
%D 1997
%P 743-748
%V 38
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a9/
%G en
%F CMUC_1997__38_4_a9
Balaj, Mircea. Separation of $(n+1)$-families of sets in general position in $\bold R^n$. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 743-748. http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a9/