Geodesic
Independence for Sets of Topological Spheres
Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 520-524

Voir la notice de l'article provenant de la source Cambridge University Press

Consider a collection of topological spheres in Euclidean space whose intersections are essentially topological spheres. We find a bound for the number of components of the complement of their union and discuss conditions for the bound to be achieved. This is used to give a necessary condition for independence of these sets. A related conjecture of Griinbaum on compact convex sets is discussed.
DOI : 10.4153/CMB-1991-082-1
Mots-clés : 52A37, 05B99 
Pakula, Lewis; Schwartzman, Sol. Independence for Sets of Topological Spheres. Canadian mathematical bulletin, Tome 34 (1991) no. 4, pp. 520-524. doi: 10.4153/CMB-1991-082-1
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[1] 1. Assouad, P., Densité et dimension, Ann. Inst. Fourier (Grenoble) (3)33 (1983), 233–282. Google Scholar

[2] 2. Griinbaum, B., Venn diagrams and independent families of sets, Mathematics Magazine 48 (1975), 12–22. Google Scholar

[3] 3. Marczewski, E., Indépendance d'ensembles et prolongements de mesures, Colloq. Math. 1(1947), pp. 122— 132. Google Scholar

[4] 4. Massey, W. S., Singular Homology Theory. Springer-Verlag, 1980. Google Scholar

[5] 5. Pakula, L., A note on Venn diagrams, American Math. Monthly (1)96 (1989), 38–39. Google Scholar

[6] 6. A. Rényi, C. Rényi and J. Surânyi, Sur l'indépendance des domaines simples dans l'espace Euclidien à n dimensions, Colloq. Math. 2 (1951), 130–135. Google Scholar

[7] 7. Spanier, E., Algebraic Topology. McGraw-Hill, Inc., 1966. Google Scholar

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