A Hausdorff compact space is metrizable if and only if it is a continuous open image of the Sorgenfrey line

Vlad Smolin

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arXiv · 2110.12808

A Hausdorff compact space is metrizable if and only if it is a continuous open image of the Sorgenfrey line

Vlad Smolin

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Abstract

In this note we prove that a regular continuous open image of the Sorgenfrey line with an uncountable weight has a closed subspace that is homeomorphic to the Sorgenfrey line. As a corollary we deduce the theorem in the title.

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Vlad Smolin. 2021-10-25. A Hausdorff compact space is metrizable if and only if it is a continuous open image of the Sorgenfrey line. https://arxiv.org/abs/2110.12808

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