On one-to-one continuous images of R

Academic Article

Abstract

  • One-to-one continuous images of the reals play an important role in dynamical systems as all non-periodic orbits fall in this class. We present a characterization of one-to-one continuous images of the reals in the realm of hereditarily unicoherent spaces. The characterization is reminiscent of the well-known characterization of the reals which requires each point to be a cut point of order 2. As a particularly useful corollary we obtain a characterization of the non-compact one-to-one continuous images of the halfline. © 1991.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Aarts JM; Oversteegen LG
  • Start Page

  • 17
  • End Page

  • 23
  • Volume

  • 41
  • Issue

  • 1-2