Vol. 79, No. 1, 1978

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ISSN: 0030-8730
The space of ANR’s of a closed surface

Laurence Richard Boxer

Vol. 79 (1978), No. 1, 47–68
Abstract

We study the hyperspace (denoted 2hM) of ANR’s of a (polyhedral) closed surface M. The topology of 2hM is induced by Borsuk’s homotopy metric. We show the subpolyhedra of M are dense in 2hM. We obtain a necessary and sufficient condition for an arc in 2hM joining two points. We show that 2hM is an ANR (). We prove that the subspace of 2hM whose members are AR’s has the homotopy type of M.

Mathematical Subject Classification 2000
Primary: 54C55
Secondary: 57N99
Milestones
Received: 26 April 1977
Revised: 5 January 1978
Published: 1 November 1978
Authors
Laurence Richard Boxer