Vol. 93, No. 2, 1981

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Detecting the disjoint disks property

Robert Jay Daverman

Vol. 93 (1981), No. 2, 277–298
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
Authors
Robert Jay Daverman