Continuous decompositions into cells of different dimensions

John J. Walsh and David Clifford Wilson

Vol. 110 (1984), No. 1, 223–232

DOI: 10.2140/pjm.1984.110.223

Abstract

In 1970 S. Jones showed that the only continuous decomposition of Eⁿ into points and k-cells is the trivial decomposition into points. This is extended by showing that, for a pair of positive integers r, s with r + s ≥ n, the only continuous decomposition of Eⁿ into points, r-cells, and s-cells is the trivial decomposition into points.

Mathematical Subject Classification 2000

Primary: 54B15

Secondary: 57N99

Milestones

Received: 26 February 1982

Published: 1 January 1984