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}
}