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arXiv · 2007.08845

Open images of the Sorgenfrey line

Vlad Smolin
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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.

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Vlad Smolin. 2020-07-17. Open images of the Sorgenfrey line. https://arxiv.org/abs/2007.08845

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