Factored codimension one cells in Euclidean n-space

Robert Jay Daverman

Vol. 46 (1973), No. 1, 37–43

DOI: 10.2140/pjm.1973.46.37

Abstract

Seebeck has proved that if the m-cell C in Euclidean n-space Eⁿ factors k times, where m ≦ n − 2 and n ≧ 5, then every embedding of a compact k-dimensional polyhedron in C is tame relative to Eⁿ. In this note we prove the analogous result for the case m + 1 = n ≧ 5 and n − k ≧ 3. In addition we show that if C factors 1 time, then each (n − 3)-dimensional polyhedron properly embedded in C can be homeomorphically approximated by polyhedra in C that are tame relative to Eⁿ.

Mathematical Subject Classification

Primary: 57A45

Milestones

Received: 5 January 1972

Published: 1 May 1973