Detecting the disjoint disks property

Robert Jay Daverman

Vol. 93 (1981), No. 2, 277–298

DOI: 10.2140/pjm.1981.93.277

Abstract

This paper explores conditions under which a metric space S satisfies the following Disjoint Disks Property: any two maps of the standard 2-cell B² into S can be approximated by maps having disjoint images. Among its many applications, it provides a proof that if Y is the cell-like image of an n-manifold (n ≥ 3), then Y × E² has the Disjoint Disks Property, which implies that Y × E² is a manifold. It adds further evidence for the unifying force of this property by giving comparatively easy proofs for established facts about certain decomposition spaces that are manifolds.

Mathematical Subject Classification 2000

Primary: 57N15

Secondary: 54B15

Milestones

Received: 27 August 1979

Revised: 2 January 1980

Published: 1 April 1981