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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

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