Separation of $(n+1)$-families of sets in general position in $\bold R^n$
Balaj, Mircea
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 743-748 / Harvested from Czech Digital Mathematics Library
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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 $S_n^+$.

Publié le : 1997-01-01
Classification:  47H10,  52A37 
@article{118969,
     author = {Mircea Balaj},
     title = {Separation of $(n+1)$-families of sets in general position in $\bold R^n$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {743-748},
     zbl = {0946.52002},
     mrnumber = {1603706},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118969}
}

Balaj, Mircea. Separation of $(n+1)$-families of sets in general position in $\bold R^n$. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 743-748. http://gdmltest.u-ga.fr/item/118969/

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