Vol. 25, No. 3, 1968

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ISSN: 0030-8730
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