No arc-connected treelike continuum is the 2-to-1 image of a continuum

Volume 180 / 2003

Jo Heath, Van C. Nall Fundamenta Mathematicae 180 (2003), 11-24 MSC: Primary 54C10. DOI: 10.4064/fm180-1-2

Abstract

In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.

Authors

  • Jo HeathMathematics Department
    Parker Hall
    Auburn University
    Auburn, AL 36849-5310, U.S.A.
    e-mail
  • Van C. NallDepartment of Mathematics and Computer Science
    University of Richmond
    Richmond, VA 23173, U.S.A.
    e-mail

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