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

2021/10/25 by Smolin, Vlad
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2110.12808

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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• Closed and open-closed images of submetrizable spaces
• Extending continuous functions
• An Algebraic and Logical approach to continuous images
• Function spaces on separable compact lines