Vol. 18, No. 1, 1966

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Subsets of n-books in E3

C. A. Persinger

Vol. 18 (1966), No. 1, 169–173

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.

Mathematical Subject Classification
Primary: 54.78
Received: 15 March 1965
Published: 1 July 1966
C. A. Persinger