Rigid sets in Eⁿ

David G. Wright

Vol. 121 (1986), No. 1, 245–256

DOI: 10.2140/pjm.1986.121.245

Abstract

We construct rigid embeddings of Cantor sets in Eⁿ (n ≥ 3) and rigid embeddings of compacta in Eⁿ (n ≥ 3). In each case there are uncountably many different rigid embeddings. The results in this paper generalize three-dimensional theorems by Sher, Shilepsky, Bothe, Martin, and Brechner and Mayer.

Mathematical Subject Classification 2000

Primary: 57M30

Secondary: 54F15, 57N15

Milestones

Received: 9 July 1984

Published: 1 January 1986