Vol. 46, No. 1, 1973

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Factored codimension one cells in Euclidean n-space

Robert Jay Daverman

Vol. 46 (1973), No. 1, 37–43
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
Authors
Robert Jay Daverman