Open images of the Sorgenfrey line

摘要

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 space X, which contains a dense and co-dense copy of the Sorgenfrey line, can be the continuous open image of the Sorgenfrey line. It follows 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.(c) 2021 Elsevier B.V. All rights reserved.