Defining subsets of E³ by cubes

Richard Benjamin Sher

Vol. 25 (1968), No. 3, 613–619

DOI: 10.2140/pjm.1968.25.613

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