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Independence for Sets of Topological Spheres

Published online by Cambridge University Press:  20 November 2018

Lewis Pakula  and
Sol Schwartzman
Lewis Pakula
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston RI, USA 02881
Sol Schwartzman
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston RI, USA 02881
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Abstract

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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.

Keywords

52A3705B99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 520 - 524
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Assouad, P., Densité et dimension, Ann. Inst. Fourier (Grenoble) (3)33 (1983), 233–282.Google Scholar
2. Griinbaum, B., Venn diagrams and independent families of sets, Mathematics Magazine 48 (1975), 12–22.Google Scholar
3. Marczewski, E., Indépendance d'ensembles et prolongements de mesures, Colloq. Math. 1(1947), pp. 122— 132.Google Scholar
4. Massey, W. S., Singular Homology Theory. Springer-Verlag, 1980.Google Scholar
5. Pakula, L., A note on Venn diagrams, American Math. Monthly (1)96 (1989), 38–39.Google Scholar
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. Spanier, E., Algebraic Topology. McGraw-Hill, Inc., 1966.Google Scholar