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Abstract
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An n-book Bn in E3 is
defined to be the union of n closed disks in E3 such that each pair of disks meets
precisely on a single arc B on the boundary of each. The disks are called the leaves of
Bn, and the arc B is its back.
The zero-dimensional subsets of a tame n-book in E3 are shown to be limited by
the fact that no wild Cantor set lies in such a book, even if the number of leaves is
countable. However, wild arcs and disks abound in tame n-books. Each arc in a
tame n-book is shown to lie in a tame 3-book in E3, and the tame disks
in tame n-books are shown to be characterized by the tameness of their
boundaries.
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Mathematical Subject Classification
Primary: 54.78
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Milestones
Received: 15 March 1965
Published: 1 July 1966
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