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A degree-zero, monotone, surjective self-map of the Pontryagin surface

Volume 254 / 2021

Robert J. Daverman, Thomas L. Thickstun Fundamenta Mathematicae 254 (2021), 305-312 MSC: Primary 54B15; Secondary 54C10, 54G99, 57N60. DOI: 10.4064/fm766-1-2021 Published online: 19 April 2021


This paper presents an example, as promised by the title, of a degree-zero, monotone, surjective map of the standard Pontryagin surface to itself. This exposes the need for some hypothesis concerning degree in results about when monotone self-maps of the Pontryagin surface can be approximated by homeomorphisms.


  • Robert J. DavermanDepartment of Mathematics
    University of Tennessee
    Knoxville, TN 37996, U.S.A.
  • Thomas L. ThickstunDepartment of Mathematics Texas State University
    San Marcos, TX 78666, U.S.A.

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