English

Open images of the Sorgenfrey line

General Topology 2020-07-20 v1

Abstract

We give a description of Hausdorff continuous open images of the Sorgenfrey line: these are precisely those spaces that have a Sorgenfrey base. Using this description we prove that no Hausdorff compact space that contains a copy of the Sorgenfrey line is a continuous open image of it; in particular the double-arrow space is not a continuous open image of the Sorgenfrey line.

Keywords

Cite

@article{arxiv.2007.08845,
  title  = {Open images of the Sorgenfrey line},
  author = {Vlad Smolin},
  journal= {arXiv preprint arXiv:2007.08845},
  year   = {2020}
}