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Degree-one, monotone
self-maps of the Pontryagin surface are
near-homeomorphisms
Robert J. Daverman and Thomas L. Thickstun |
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Vol. 303 (2019), No. 1, 93–131
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Abstract |
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We prove that a self-map of the closed Pontryagin surface can be approximated by homeomorphisms if and only if it is monotone and has degree . This adds to a body of theorems, each of which characterizes for some space or class of spaces those self-maps which are approximable by homeomorphisms. |
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Keywords
Pontryagin surface, Pontryagin disk, monotone map,
near-homeomorphism, degree-one map, figure-eight,
shrinkability criterion
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Mathematical Subject Classification 2010
Primary: 57N05, 57P05
Secondary: 54B15, 54G99, 57N60
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Milestones
Received: 19 June 2017
Revised: 27 March 2019
Accepted: 4 April 2019
Published: 21 December 2019
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Authors |
| Robert J. Daverman | |
| Department of Mathematics University of Tennessee Knoxville, TN United States |
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| Thomas L. Thickstun | |
| Department of Mathematics Texas State University San Marcos, TX United States |
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