Metrizable images of the Sorgenfrey line

Mikhail Patrakeev

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arXiv · 1401.2289

Metrizable images of the Sorgenfrey line

Mikhail Patrakeev

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Abstract

We give descriptions of metrizable topological spaces that are images of the Sorgenfrey line under continuous maps of different types (open, closed, quotient and others). To obtain this descriptions, we introduce the notion of a Lusin pi-base, the Sorgenfrey line and the Baire space have Lusin pi-bases, and if a space X has a Lusin pi-base, then for each nonempty Polish space Y, there exists a continuous open map from X onto Y.

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BibTeX RIS

Mikhail Patrakeev. 2014-01-10. Metrizable images of the Sorgenfrey line. https://arxiv.org/abs/1401.2289

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