Vol. 25, No. 3, 1968

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Defining subsets of E3 by cubes

Richard Benjamin Sher

Vol. 25 (1968), No. 3, 613–619
Abstract

This paper is concerned with compact subsets of E3 which are the intersection of a properly nested sequence of compact 3-manifolds with boundary each of which is the union of a finite collection of pairwise disjoint 3-cells. Such sets are characterized by a property of their complements. Related results are stated in terms or embeddings of compact 0-dimensional sets and upper semicontinuous decompositions of E3.

Mathematical Subject Classification
Primary: 54.78
Milestones
Received: 28 August 1967
Published: 1 June 1968
Authors
Richard Benjamin Sher